{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "###### Content under Creative Commons Attribution license CC-BY 4.0, code under BSD 3-Clause License © 2019 Lorena A. Barba, Tingyu Wang" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Transform all the vectors\n", "\n", "This is the first lesson in the module titled **\"Land on Vectors Spaces\"**, for learning practical linear algebra with Python. We take a visual and intuitive approach to illuminate some of the core ideas in linear algebra, enabled by computing. \n", "\n", "Linear algebra is a surprisingly useful subject, at the heart of computer graphics, cryptography, and machine learning. It is applied in data compression, game theory, and understanding networks. Engineering applications of linear algebra are everywhere: electric circuits, statics and dynamics, digital signal processing, optimization, robotics, multi-body dynamics… you name it!\n", "\n", "Whether you missed out on taking a college linear algebra course, or you did so a long time ago and need a refresher, this learning module can be your launching pad to the wonderful world of _vector spaces_.\n", "\n", "Let's get started! We will be using our favorite libraries of the Python ecosystem: NumPy and Matplotlib. We also have a few helper functions in the `plot_helper.py` script, which will make it easy to visualize the ideas in these lessons. \n", "Go ahead and load these by executing the next two cells." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy\n", "%matplotlib inline\n", "from matplotlib import pyplot" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If you don't have the plotting script locally, you can get it by adding a code cell and executing this code in it.\n", "\n", "```Python\n", "from urllib.request import urlretrieve\n", "URL = 'https://go.gwu.edu/engcomp4plot'\n", "urlretrieve(URL, 'plot_helper.py')\n", "```" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import sys\n", "sys.path.append('../scripts/')\n", "\n", "# Our helper, with the functions: \n", "# plot_vector, plot_linear_transformation, plot_linear_transformations\n", "from plot_helper import *" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Vectors\n", "\n", "### What's a vector?\n", "\n", "Vectors are everywhere: physics, engineering, mathematics, computer science, video games, and more. Each field's interpretation of what a vector *is* may be different, but vectors live a similar life in every space.\n", "\n", "The first episode in the wonderful video series, [_\"Essence of Linear Algebra\"_](http://3b1b.co/eola) tells you of three different ideas about vectors [1]:\n", "\n", "1. For physicists, a vector is an \"arrow\" of a given length (magnitude) and direction. It can represent directional quantities like velocity, force, acceleration.\n", "2. For computer scientists, a vector is an ordered list of numbers. It can represent a set of variables or features stored in order.\n", "3. For mathematicians, vectors are generic objects that behave a certain way when they are added or scaled: $\\mathbf{u}+\\mathbf{v}$, $\\alpha\\mathbf{v}$.\n", "\n", " \n", "#### How you think of a vector depends on who you are..." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In physics, vectors are almost always two- or three-dimensional (although in some fancy branches of physics they do go to higher dimensions). Vectors help physicists describe things like motion and electro-magnetic fields on a plane or in physical 3D space.\n", "\n", "In computer science and in data science, vectors are often multi-dimensional, that is, they have many components. They contain a set of ordered variables in a data model, like for example: the age, weight, daily hours of sleep, weekly hours of exercise, and blood pressure of an individual (five dimensions)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Visualizing vectors\n", "\n", "Let's start with the idea of a vector as an \"arrow\" (magnitude plus direction). We visualize a vector by placing this arrow with its tail at the origin of a coordinate system.\n", "But changing the position of the tail doesn't change the vector's magnitude or direction, so the vector is the same no matter where we draw it. \n", "\n", "In the code cell below, we define a list with a single vector of coordinates $(2, 2)$, and we use our custom function `plot_vector()` to plot the vector with its tail at four different positions on a 2D coordinate system. " ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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OYXPyc13Dhg1rir952ii+uRJPSUmhR48epKWleV0KACUlJeTl5fmqJmgZdS1btoykpCRuv/12AMrKygCYM2cObdq04dFHH6VLly773ea6devqXF5QUBAO+uzsbLKzs+tcv7m0hGPYnPxclx/4JsQTExNJS0sjIyPmfxy63vxYEwS/runTpzN9+vTw9KZNmzjyyCOZOXMmQ4YMqff2unfvXufy9PS9f+M3NTXVV/sr6Mewufm1Lj/wz2cTERGJmkJcPHXdddcxfvz4fR6LSP34ZjhF4tPDDz/sdQkigaYrcRGRAFOIi4gEmEJcRCTAFOIiIgGmEBcRCTCFuIhIgCnERUQCTCEuIhJgCnERkQBTiIuIBJhCXEQkwBTiIiIBphAXEQkwhbiISIApxEVEAkwhLiISYApxEZEAU4iLiASYQlxEJMAU4iIiAaYQFxEJMIW4iEiAKcRFRAJMIS4iEmAKcRGRAFOIi4gEWJLXBUj8WbRoEbNmzWL37t3s2rWLXbt2ceONN3LhhRd6XZpI4CjEpdk98cQTTJgwgUmTJgGwePFizj//fI455hiOO+44j6sTCRYNp0izu+eee5gwYUJ4esiQIYRCITZu3OhhVSLBpCtxaXZ9+/YNP/7pp5+YMWMGPXr04Iwzzoiqnc2bN9e5PD8/v0H1iQSJb0K8oqKCkpISr8sIKykp8V1N0LLqmjJlCgsXLqR79+689NJLWGspKiqq9/OzsrLqvW5paWlUbcdSSzqGzcHPdWVkZHhdBsZa63UNACxZssSmpqaSkOCPEZ5QKERpaSl+qgn8WVdxWTmrvyygT6e2UddVUVHB3LlzeeONN3jsscdo165dvZ87dOjQeq87f/582rdvX+/1Y8mPxxBUV7RCoRDDhg0zXtfhmyvxlJQUevToQVpamtelAM67bF5enq9qAn/VVVb+E7NfXcGMhcuYde2FpLCrQXWdeOKJ9OzZk3feeYfp06fX+3nr1q2rc3lBQUE46LOzs8nOzo6qrljx0zGMpLqi45dPBr4J8cTERNLS0nzx8aSSH2sC7+uqqAjx4rKV3PrsIr7euoMz+x3LiH7HkZubW6+6ysvLadWqVZV5Rx99NBs3bozqNXXv3r3O5enp6eHHqampvjqOXh/D2qiu4PFNiIv/WWt5beUaps36B59/uSU8/97LLoiqnT59+rBmzZoq8/Lz8zn11FObpE6ReOKfASbxtQ/XfsmQ6/7MOX98tEqA/3L4yZzQtf5fMAKsXbuWpUuXhqdfeOEFvvjiCy655JImq1ckXuhKXOr07fYfuGbmf/OPdz/eZ1lyUiJ3/2Z01G0+8sgj3HPPPdx3331UVFRgjOGVV15h4MCBTVGySFxRiEudDmvXhtsmnUu7A9OZtfTdKst+N3oIRx52SNRtXnPNNVxzzTVNVaJIXNNwitTJGENm2za8t6bqT1NmpLbm5olne1SViFRSiEudtu4oZOiUB1n3VT7JSYlcOOREAG4YP5JDD9KdAiJe03CK1Kp6gC+8/QoG9OzC+2s28l/jhntdnoigEJda1BTgoweeAMDiP11NWsoBHlcoIqDhFKlBXQEO0Du7k4fViUgkhbhUsb8AFxF/UYhLmAJcJHgU4gIowEWCSiEuCnCRAFOIxzkFuEiwKcTjmAJcJPgU4nFKAS7SMijE45ACXKTlUIjHGQW4SMuiEI8jCnCRlkchHicU4CItk0I8DijARVouhXgLpwAXadkU4i2YAlyk5VOIt1AKcJH4oBBvgRTgIvFDId7CKMBF4otCvAVRgIvEH4V4C6EAF4lPCvEWQAEuEr8U4gGnABeJb0leFyANF+QAX7BgAbNnz6aiooLCwkI6derEjBkzOOqoo7wuTSRQdCUeUNt2FgU2wAEmTpzI1KlTWb58OStXriQjI4MzzzyTsrIyr0sTCRSFeADtKN7FObc8EdgABxg9ejQjRowAICEhgauvvpoNGzawevVqjysTCRYNpwTMtp1FTJm7nK+2FwY2wAEWLlxYZbp169YAlJeX17uNzZs317k8Pz8/+sJEAsY3IV5RUUFJSYnXZYSVlJT4rqZtO4s466bHnABPTOT5GyYx7PguFBUVeV1ao/fXW2+9xWGHHUavXr3q/XqysrLq3X5paakv9hP4s2+B6opWSUkJGRkZXpfhnxDftWsXa9euJSHBHyM8oVDIVzXtKN4VvgJPSjDcOrY/mcm7yc3N9bo0oHH7q7y8nAceeIArrriCzz77LCb1bdiwgcLCwpi0HS2/9S2Agh+KWbxqI+NOOspXdYE/9xc4dWVmZnpdhn9CPCUlhR49epCWluZ1KYDzLpuXl+eLmrbtLGLyLU+Er8BvuaA/l40Z4XldkRqzvyZPnsxFF13ElClTonreunXr6lxeUFDA0KFDAcjOziY7Ozuq9mPFT33r+8JiZixYzuxX32fGpaM4ML2VL+qK5Kf9Fckvnwx8E+KJiYmkpaX54uNJJT/UtHVHIefd9hRffLOV5CRnCCUzebfnddWkIftr2rRppKSkMGPGDIwxUW2ve/fudS5PT08PP05NTfXV/vK6b5Xs2s1f/r6MB+a/TlFpGT2P7MCkkQP45JOPW0zfihe+CXHZV033gQ87votvhlAa6/7772fTpk387W9/wxgTfl19+/b1uLKW66c9e3jm1fe5c+5iCnbsHV6677ILSEz0z1CF1J9C3Kdq+0Eev3w511hPPvkk8+bNY9asWeHbCpcsWULnzp0V4jFgreXvb+dy8zP/ZMPmbVWWndYrm7NPOY7i4mKPqpPGUIj7UJB/ErM+ioqKuOqqqwiFQgwYMKDKsmeffdajqlqu8p/28NsZc3nhf1fWuPz+K8ZGPZQl/qEQ95mWHuAAGRkZVFRUeF1G3GiVnMTzf/wNF59xCuf88VH2VITCy8YM6s0pPfSrDoJMg2A+Eg8BLt7YtrOI6x5bUCXAExIMf7r0fA+rkqagEPcJBbjESvW+NXvqJBITEvjtWQPp3ukwr8uTRtJwig8owCVWautbr6z4lNsvOdfr8qQJKMQ9pgCXWKmrb8254RLatUnfTwsSBBpO8ZACXGJlf31LAd5yKMQ9ogCXWFHfii8KcQ/oJJNYUd+KPwrxZqaTTGJFfSs+KcSbkU4yiRX1rfilEG8mOskkVtS34ptCvBnoJJNYUd8ShXiM6SSTWFHfElCIx5ROMokV9S2ppBCPEZ1kEivqWxJJIR4DOskkVtS3pDqFeBPTSSaxor4lNVGINyGdZBIr6ltSG4V4E9FJJrGiviV1UYg3AZ1kEivqW7I/CvFG0kkmsaK+JfWhEG8EnWQSK+pbUl8K8QbSSSaxor4l0VCIN4BOMokV9S2JlkI8SjrJJFbUt6QhFOJR0EkmsaK+JQ2lEK8nnWRNr7y8nD/+8Y8kJSWxadMmr8vxjPqWNIZCvB50kjW9TZs2MXjwYL799lsqKiq8Lscz6lvSWArx/di2s0gnWQwUFxczb948fv3rX3tdimfUt6QpKMTrsKN4F+fc8oROshjo2bMnXbt29boMz6hvSVNJ8roAv9q2s4gpc5fz1fZCnWQ+tXnz5jqX5+fnN1Ml0VHfkqbkmxCvqKigpKTE6zLCQnvKSW+dTHJiIs/fMIlhx3ehqKjI67IoKSnx3b6ChtdVWloKOMMr0e7frKysqLbjh+O3bWcRZ930mBPg6lv14ue6MjIyvC7DPyG+a9cu1q5dS0KCP0Z4QqEQt53fj29+LCMzeTe5ublelwQ4dfltX0HD61q/fj0Aa9asYfv27bEqjw0bNlBYWBiz9utjR/Gu8BV4UoLh1rH91bfqwc91ZWZmel2Gf0I8JSWFHj16kJaW5nUpgPMum5eXx2mn9vdNTbC3Lj/tK2h4XZVX4j179uSII46Iapvr1q2rc3lBQQFDhw4FIDs7m+zs7Kjab0rbdhYx+ZYnwlfgt1zQn8vGjGgRxzDW/FyXH/gmxBMTE0lLS/PFx5NKfqwJWlZdqampAKSnp0f9erp3717n8vT09Crb8Wp/bd1RyHm3PcUX32wlOckZQslM3t1ijmFz8GtdfuCfzyYiLVBN94Gfc0pPr8uSFsQ3V+ISX8rLyxkxYgQ//PADAOPHjycrK4uFCxd6XFnTqe0HefzwJaa0HApx8USrVq3IycnxuoyY0U9iSnPRcIpIE1OAS3NSiIs0IQW4NDeFuEgTUYCLFxTiIk1AAS5eUYiLNJICXLykEBdpBAW4eE0hLtJACnDxA4W4SAMowMUvFOIiUVKAi58oxEWioAAXv1GIi9STAlz8SCEuUg8KcPErhbjIfijAxc8U4iJ1UICL3ynERWqhAJcgUIiL1EABLkGhEBepRgEuQaIQF4mgAJegUYiLuBTgEkQKcREU4BJcCnGJewpwCTKFuMQ1BbgEnUJc4pYCXFoChbjEJQW4tBQKcYk7CnBpSRTiElcU4NLSKMTFMy+//DInnngigwYNYvDgweTl5cV0ewpwaYmSvC5A4tNHH33EpEmTWLVqFd26deP5559n5MiRrFu3joyMjCbf3vYfi7ngPgW4tDy6EhdP3H///Zx99tl069YNgIkTJ7Jnzx7mzp0bk+1d8sA8Bbi0SApx8cTy5cs56aSTwtMJCQn07duXZcuWxWR7X377nQJcWiTPh1OMMUlA5oIFC9iyZQvp6elelwRAcXEx3333na9qgpZR186dO/nxxx9p1aoVmzdvDs/PyMjg008/rTKvLvn5+XUu/za/IPw4saKMJ668hL6dD6l3+7HSEo5hc/JzXcccc8zhQIG1do9XdRhrrVfbdgow5nDgG0+LEBFpuCxrrWdXBn4YTsn0ugARkUbwNMM8H04BvgPIzMxk7ty5dOrUyet6+O6777jwwgsBfFMT+Kuur7bu4OGX3+JfK/Po9LOD2P3Ry5go6urXrx+TJ0/mN7/5TXjeFVdcQVJSEo899li9aigoKKhz+fr167niiisAeOGFF+jbt2+92o0lPx3DSKorOpV1uX3wOy9r8UOIV4BzQnbq1Inu3bt7XQ/p6enhgPBLTeCPurbuKOTueUt4avE77KkIQet0bv31BVz2yhNR1TV8+HC+/vrr8LrWWtavX8/NN99c79e1v/XS0tLCjzt27OiL4+iHY1gT1RWdyLpwM8wrfghxCYCi0jL+/D9v8OCC/6WkbHd4fv9jj2Jk325Rtzdt2jSGDx/O+vXrOfroo3nxxRdJTEzkkksuacqyRVo8hbjUqfynPTy1+B3unreU734o2mf5/ZePxRgTdbv9+vVj7ty5TJgwgZSUFBISEnj99ddj8oM+Ii2ZQlzq9GPJLkIhS5cOh+4T4uf278WgXtkNvmVvzJgxjBkzpinKFIlbfrg7RXzs0IMyuGrMEDr9rG2V+cYY7r1MASziNYW41GlPRQW/nP4MC3JWAdC9k3M31SUj+9PzyI5eliYiKMSlDtUD/MZfnMmi6VdxQHISd/7qPI+rExHQmLjUoqYAv/eyMRhjmDX1Yjq1b+dxhSICPghx98dVTU5Oju3Y0R8fzw8//HAKCwvJzc3FLzVB89VVV4ADXDyivyd1Reuwww4LP87M9McPBvt1X6mu6FTWlZGREf2tWU1MwylSxf4CXET8RSEuYQpwkeBRiAugABcJKoW4KMBFAkwhHucU4CLBphCPYwpwkeBTiMcpBbhIy6AQj0MKcJGWw7chHgqF6NevH507d/a6FHbv3s3tt9/O4MGDGT58OL1792bMmDF8+eWXntW0Y8cO7rjjDgYOHMiQIUM44YQTmD59Onv21P33WpsrwDds2MCAAQMYMmRIk7Ybjddeey38+OKLLyYvL8+zWiKVl5cza9YsDj74YDZt2uR1OQAsWLCA0aNHM2XKFAYPHszYsWM97d8AixYt4txzz2X06NFcc801nHbaaSxYsMDTmqozxlxjjLHGmCFe1eD5T2zW5rHHHmPDhg20adPG61LYuXMns2bN4uOPP6Z9+/aEQiHGjx/PRRddxL///W9PanrjjTdYuHAhK1asoE2bNnz77bf06dOH8vJy7rrrrhqf01wBPm/ePB5//HESExObtN1ofPTRR1x33XXh6bFjxzJy5EjWrVvn6e8s37RpExdeeCEHH3wwFRWe/kGYKiZOnMiCBQs46KAovSfQAAATeElEQVSD6N27N9deey1nnnkmn332Ga1bt/akpieeeIIJEyYwZswYcnNz2bZtG7/4xS845phjOO644zypKVJ+fj7AVK/r8OWV+JYtW3jmmWe4/PLLvS4FgLZt27J06VLat28PQEJCAoMGDWL9+vWe1nT99deH3+Q6dOjAuHHjmD9/fo3rN+cQSrt27Xj77bfp2rVrk7ddX/fffz/Dhg0LT48aNYo9e/Ywd+5cz2oCKC4u5umnn+ass87ytI7qRo8ezemnnw44/fvqq69mw4YNrF692rOa7rnnHiZMmBCeHjhwIKFQiI0bN3pWU6Q//OEPAPd6XYcvQ/z3v/899957LykpKV6XAkCrVq3o3bt3eHrLli3MnTuXa6+91rOaRowYUeWPDAO0bt2a8vLyfdZt7jHws88+m1atWsWk7fpavnw5xx9/fHg6ISGBvn37smzZMg+rgp49e9KlSxdPa6jJwoULq0xXXn3X1J+aS9++fUlKcgYL9uzZwyOPPEKPHj0444wzPKup0uLFiytr+5fXtfguxCt3jt+uVMAJ7759+9KlSxdGjhxZ67CFVz744AN+/vOfV5kXj19ifv/99/z444/87Gc/qzI/MzPT83HeoPjggw/o0KEDp556qtelMGXKFM4//3zefvttXn/9ddLT0z2tp6SkhJtvvpn77rvP0zoq+SrEi4uLuemmm3j44Ye9LqVGHTt2JDc3ly+//JI33niDyy67zOuSwt58802+/vprbrnllvC8eAxwgNLSUoB9Pg0ccMAB4WVSu927dzNjxgxmzpxJcnKy1+Xw0EMPsWjRIgYPHsypp55aORbtmVtvvZXJkyf75jdjNkuIG2PucL/BrfXfF198wfTp05k8eXKVXyEaS3fccQfGmBr/HXjggQwdOrTGMcEOHTpw7733Mnv27Ca/46Gumirr+uKLL6o8Z8uWLUyePJlFixaFx8ibOsAbUpdXUlNTgX2HAnbv3h1eJrW79tprGTduHGPHjvW6lLDExERuuukmrLU89NBDntXx8ccfs3LlSiZPnuxZDdU1190pfwaerGuFrl275v/1r3/l888/D4/Pbdq0iYKCAoYMGULXrl2ZPXt2kxY1derUWg9GcXExn332Gb169QrfRRB5t0W3bt0AWLt2Lccee2yz1FRZ11dffRWe3rFjB6NGjeLxxx+nT58+QGyuwKOty0vt2rWjTZs2bNu2rcr8goICjjrqKI+qCoann36a5ORk7rnnHq9Loby8vMqnqYSEBLKzs1m7dq1nNS1ZsoRdu3YxbNiwylyovJPgYWPMD8Cl1tpm/ea1WULcWlsMFNe1Tk5ODitWrKhy+9cdd9zBc889R05OTkzqSk9Pr3V8raioiLZt25KUlMS8efPYvn07U6fuvZuo8iNdhw4dmq2myroq/7p8UVER5513HrfddhvDhw8H4IknnyJnq2nyIZRo6vKDYcOG8dlnn4WnrbWsXr2am2++2cOq/O0vf/kLBQUFvPzyyxhjyM3NBZwvGL3Qp08f1qxZU2Vefn6+p+P0t956K7feeivg9PkDDzxwPPB/wHXW2hwvavLVmLifzZkzh+3btwNQVlbG3XffTc+ePTnppJM8qaesrIxRo0Zxyimn0LFjR1atWsWHKz/iphf+N+7GwGsybdo03nzzzfD04sWLSUxM5JJLLvGwKv968sknmT9/PmPHjuWTTz5h1apVLF68mM8//9yzmtauXcvSpUvD0/Pnz+eLL77QMazOWuuLf2+99ZYtLCy01lqbn59vBw8ebI844gh7wAEH2MGDB9tnn33WNqfCwkJbWdPXX39tr776atu7d287aNAg27t3bztx4kT79ddfN2tNkXX9+c9/tsDef8ZYegyzDLnMMuQye+NTL9lQKNTsdRUWFtpFixbZwYMH2/bt29s2bdrYwYMH29mzZzdbLZWefvrp8P458cQT7Zo1a5q9hup2795tBw4caLt06WIBe/LJJ9tx48Z5WlNhYaFNSEio2p/cf8193kWaOXOm7d+/v+3fv7899thj7cknn2yXLFniWT3VXXnllRb40N1XnwDzrQfZaay1Hrx17CsnJ8f27dvX05+mi1RUVERubi5+qglqrssPd6H4cX9t3ryZrKwsANatW0f37t09rsjhx30FqitaRUVF+hub0nh+CHAR8Y5CPMCCHOB++AVZIi2BQjygghzg8+bNY9KkSSQkqPuJNJbOogCqCIW49MEXAxng4I9fkCXSUvj2V9FKzfZUVDD9HyvIyfsaCF6Ag/MLsprC/u5L9/rHs0Wag29CvKKigpKSEq/LCCspKfFdTXsqKvjV/c+HA/y/xg7lpvHDKS6u8+eomkVD9tdPP/1ERUUFRUVFDdpm5Z0n9VFaWtrg7TQ1P/YtUF3RKikp8cXdMr4J8V27drF27VrfjJOGQiFf1VQRClW5Ah8/4BjOOzbT09/3HKkh++v7778P3z4Waxs2bKCwsDDm26kPv/WtSn6sq7isnNVfFtCnU1tf1QXO/vLDL8HyTYinpKTQo0cP0tLSvC4FcN5l8/LyfFHTnooKLn3wxXCAXzSgOw9dPd7zX8kZ6c477+TBBx+sc52cnJzw73cBZ2y8pKSkwT/WvW7dujqXFxQUMHToUACys7PJzs5u0Haamp/6ViQ/1VVW/hOzX13BjIXLmHXthaSwyxd1RfLLJwPfhHhiYiJpaWm++HhSyQ81Vd6F8o/3PgWcIZTzjs0kPT3dV/vq+uuvZ8CAAfTq1avWN5dDDjkk/Ev+AZKTk0lMTGzw69jfD+9E1pGamuqr/eWHvlUTr+uqqAjx4rKV3PrsIr7euoMz+x3LiH7HkZub68v95Qe+CXHZV023Ed40frhvhlAipaen07ZtW9q3b68TTaJmreW1lWuYNusffP7llvD8ey+7wMOqgkEh7lO13Qfuhy8xRZrSh2u/5ManXuKdzzZUmf/L4SdzQtcs33wh7VcKcR8K8g/y1Mcrr7zCQw89xH/+8x/KysoYMmQIF198Mb/97W+9Lk2a0bfbf+Camf/NP979eJ9lyUmJ3P2b0R5UFTwKcZ9p6QEOzl+eHzVqlNdliMcOa9eG2yadS7sD05m19N0qy343eghHHnaIR5UFi3/u15G4CHCRSsYYMtu24b01Vf8QTkZqa26e2DQ/EBYPFOI+oQCXeLN1RyFDpzzIuq/ySU5K5MIhJwJww/iRHHqQvhyvLw2n+IACXOJN9QBfePsVDOjZhffXbOS/xg33urxAUYh7TAEu8aamAB898AQAFv/patJSDvC4wmDRcIqHFOASb+oKcIDe2Z08rC6YFOIeUYBLvNlfgEvDKMQ9oACXeKMAjx2FeDNTgEu8UYDHlkK8GSnAJd4owGNPId5MFOASbxTgzUMh3gwU4BJvFODNRyEeYwpwiTcK8OalEI8hBbjEGwV481OIx4gCXOKNAtwbCvEYUIBLvFGAe0ch3sQU4BJvFODeUog3IQW4xBsFuPcU4k1EAS7xRgHuDwrxJqAAl3ijAPcPhXgjKcAl3ijA/UUh3ggKcIk3CnD/UYg3kAJc4o0C3J8U4g2gAJd4owD3L4V4lBTgEm8U4P6mEI+CAlzijQLc/xTi9aQAl3ijAA+GJK8LCAIFeNPZsWMHM2fOZNmyZSQlJfHDDz8wbtw4pk2bRlKSuqNfKMCDQ2fNfijAm9arr77KwoULWbFiBW3atOHbb7+lT58+lJeXc9ddd3ldngDbdhZx3m1PKcADQsMpdagIhbj0wRcV4E2oXbt2XH/99bRp0waADh06MG7cOObPn+9xZQKwo3gX59zyhAI8QHQlXos9FRVM/8cKcvK+BhTgTeWss87aZ17r1q0pLy+Puq3NmzfXuTw/Pz/qNuPZtp1FTJm7nK+2FyrAA8Q3IV5RUUFJSYnXZYRt/CafTzZtBeC/xg7lpvHDKS4u9rgqKCkp8d2+gsbV9d577zF69GiKioqiel5WVla91y0tLY26/Vjx4zHctrOIs256zAnwxESev2ESw47v4ot95sf9BU5dGRkZXpeBsdZ6XQMAS5YssampqSQk+GOEJxQK8Z9vtpK7aTsTT+vpmyvwUChEaWkpftpX0PC6Vq9ezX333cecOXNIT0+PaptDhw6t97rz58+nffv2UbUfK347hjuKd4WvwJMSDLeNO5VBx3Tyuqwwv+2vSqFQiGHDhnkeDL65Ek9JSaFHjx6kpaV5XQrgvMtaa7lg5FDf1AROXXl5eb7aVwB33nknDz74YJ3r5OTk0KdPn/D0t99+y+OPP85LL73ECSdE/7F93bp1dS4vKCgIB312djbZ2dlRbyMW/HQMt+0sYvItT4SvwG+5oD+XjRnheV2R/LS/Ivnlk4FvQjwxMZG0tDRffDyp5MeawJ91XX/99QwYMIBevXrVekV9yCGHhG8j3LFjBxMmTODJJ59k0KBBDdpm9+7d61weWUdqaqqv9pcfjuHWHYWcd9tTfPHNVpKTnCGUzOTdntdVEz/sL7/yz2cTCbT09HTatm1L+/btyczMrPFfZYAXFRVx3nnncdtttzF8+HAAnn76aS/Ljzs13Qd+zik9vS5LGkAhLs2qrKyMUaNGccopp9CxY0dWrVrFqlWreOqpp7wuLW7oB3laFt8Mp0h8eOaZZ8jJySEnJ4eHHnrI63LijgK85dGVuDSrq666Cmttjf8kthTgLZNCXCQOKMBbLoW4SAunAG/ZFOIiLZgCvOVTiIu0UArw+KAQF2mBFODxQyEu0sIowOOLQlykBVGAxx+FuEgLoQCPTwpxkRZAAR6/FOIiAacAj28KcZEAU4CLQlwkoBTgAgpxkUBSgEslhbhIwCjAJZJCXCRAFOBSnUJcJCAU4FIThbhIACjApTYKcRGfU4BLXRTiIj6mAJf9UYiL+JQCXOpDIS7iQwpwqS+FuIjPKMAlGgpxER9RgEu0FOIiPqEAl4ZQiIv4gAJcGirJ6wIkvuzevZs//elP5OTkkJyczPfff0/nzp158MEHOeqoo7wuzxMKcGkMXYlLs9q5cyezZs1iwYIFLFu2jNzcXJKTk7nooou8Ls0TCnBpLIW4NKu2bduydOlS2rdvD0BCQgKDBg1i/fr1HlfW/LbtLFKAS6MpxKVZtWrVit69e4ent2zZwty5c7n22ms9rKr57SjexTm3PKEAl0bTmLh4YsuWLYwaNYq8vDyuv/567rrrrqjb2Lx5c53L8/PzG1peTG3bWcSUucv5anuhAlwazTchXlFRQUlJiddlhJWUlPiuJmg5dR144IHk5OSQn5/P+PHj2bJlC48++mhU28zKyqr3uqWlpRQVFUXVfqyE9pST3jqZ5MREnr9hEsOO7+KL2lpK32ouJSUlZGRkeF0GxlrrdQ0ALFmyxKamppKQ4I8RnlAoRGlpKX6qCfxb17PPPsvzzz9f5zpPPvkk3bp122d+bm4uU6dOZc6cORx55JH13ubQoUPrve78+fPD4/BeC4VCbN/5I9/8WEbfow7zupwwv/YtP9c1bNgw43UdvrkST0lJoUePHqSlpXldCuC8y+bl5fmqJvBvXVlZWZx77rl069aN1NTUGtdp164dxjh9PjExMTy/ffv2TJ06lcTERPr27Vvvba5bt67O5QUFBeGgz87OJjs7u95tx1LlMTzt1P6+OoZ+7Vt+rssPfBPiiYmJpKWl+eLjSSU/1gT+revQQw/lyCOPrLOu5557ju3btzN16tTwvMqhhC5dukT1mrp3717n8vT09PDj1NRUX+0vvx5D1RU8/vlsInFjzpw5bN++HYCysjLuvvtuevbsyUknneRxZSLB45srcYkPp59+Orm5uYwYMYL09HSKi4s59thjefXVV2nVqpXX5YkEjkJcmlVWVlbUd6GISO00nCIiEmAKcRGRAFOIi4gEmEJcRCTAFOIiIgGmEBcRCTCFuIhIgCnERUQCTCEuIhJgCnERkQBTiIuIBJhCXEQkwBTiIiIBphAXEQkwhbiISIApxEVEAkwhLiISYApxEZEAU4iLiASYQlxEJMAU4iIiAaYQFxEJMIW4iEiAKcRFRAJMIS4iEmAKcRGRAFOIi2dCoRD9+vWjc+fOXpciElgKcfHMY489xoYNG7wuQyTQFOLiiS1btvDMM89w+eWXe12KSKApxMUTv//977n33ntJSUnxuhSRQEvyugCJP4sXLyYpKYmzzjqLlStXNridzZs317k8Pz+/wW2LBIVvQryiooKSkhKvywgrKSnxXU0Q/LqKi4uZNm0a//znPykqKmL37t1YaykqKop6m1lZWfVet7S0tEHbiIWgH8Pm5ue6MjIyvC4DY631ugZpAYwxdwC372e1k4BfAhuttY9FPO9X1trODdhmNJ03y1pb96W7SAApxKVJGGPSgfT9rLYdyAV+BELuvM5AJvAhTrhfGsU2D9/PKonAoUABUGCt3VPftkWCQiEunmrMlbiI6O4UEZFAU4iLJ4wxmcaYHOBXQKYxJscY8ytPixIJIA2niIgEmK7ERUQCTCEuIhJgCnERkQBTiIuIBJhCXEQkwBTiIiIBphAXEQkwhbiISIApxEVEAkwhLiISYApxEZEAU4iLiASYQlxEJMAU4iIiAaYQFxEJMIW4iEiAKcRFRAJMIS4iEmAKcRGRAFOIi4gEmEJcRCTAFOIiIgH2/wHxMPpfDh9/5QAAAABJRU5ErkJggg==\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "vectors = [(2,2)]\n", "tails = [(-3,-2), (-3,1), (0,0), (1,-3)]\n", "plot_vector(vectors, tails)\n", "pyplot.title(\"The same vector, with its tail at four locations.\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the 2D plane, we can see clearly the connection between the \"arrow\" idea of vector, and the \"list of numbers,\" which in this case represents the coordinates of the arrow head when the tail is at the origin of the coordinate system.\n", "\n", "The first coordinate designates the horizontal distance between head and tail, and the second coordinate designates the vertical distance between head and tail. We typically will denote horizontal and vertical axes as $x$ and $y$.\n", "\n", "In three dimensions, $x$ and $y$ are usually denoting the perpendicular axes on the horizontal plane, and the vertical axis is denoted by $z$. A 3D vector thus has three components: $(x, y, z)$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Note:\n", "\n", "Our helper function `plot_vector()` takes one or two lists as arguments: a list of vectors, and a list of tails (optional). It can plot one vector with its tail on several locations, or several vectors with their tail at one location. It can also plot several vectors with their tails at different locations, but in that case, the two lists have to match in length (if they don't, the function will give an error).\n", "\n", "##### Exercise:\n", "\n", "In a new code cell, create a list of vectors (either as tuples of coordinates, or as NumPy arrays), and plot them. The default tail position is the origin. Then create a list of tail positions, and plot the same vectors again at these positions." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Fundamental vector operations\n", "\n", "Two operations are the foundation of everything: **vector addition**, and **multiplication by a scalar** (i.e., scaling).\n", "\n", "Let's first visualize vector addition. Suppose we have two vectors: \n", "\n", "$$\n", " \\mathbf{a} = \\left[ \\begin{array}{c} -2 \\\\ 1 \\end{array} \\right], \\quad \n", " \\mathbf{b} = \\left[ \\begin{array}{c} 1 \\\\ -3 \\end{array} \\right] \n", "$$\n", "\n", "We can visualize vector addition as follows: draw vector $\\mathbf{a}$ with its tail at the origin; then draw vector $\\mathbf{b}$ with its tail on the head of $\\mathbf{a}$. If you now draw a vector from the origin to the head of $\\mathbf{b}$, that vector is $\\mathbf{a} + \\mathbf{b}$.\n", "\n", "With our helper function for plotting 2D vectors, it looks like this:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# vector addition\n", "a = numpy.array((-2,1))\n", "b = numpy.array((1,-3))\n", "origin = numpy.array((0,0))\n", "\n", "vectors = [a, b, a+b]\n", "tails = [origin, a, origin]\n", "plot_vector(vectors, tails)\n", "pyplot.title(\"Adding vectors with coordinates $(-2, 1)$ and $(1,-3)$.\\n\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this visualization of vector addition, the head of $\\mathbf{a} + \\mathbf{b}$ ends up at the coordinates resulting from adding the tail-to-head horizontal and vertical distances of $\\mathbf{a}$ and $\\mathbf{b}$. In other words, from adding the respective coordinates:\n", "\n", "$$\n", " \\left[ \\begin{array}{c} -2 \\\\ 1 \\end{array} \\right] + \n", " \\left[ \\begin{array}{c} 1 \\\\ -3 \\end{array} \\right] =\n", " \\left[ \\begin{array}{c} -2+1 \\\\ 1-3 \\end{array} \\right]\n", "$$\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's now look at multiplication by a scalar: essentially, the length of the vector is *scaled* by the scalar factor. If you multiply a vector by $2$, its length (magnitude) doubles. \n", "\n", "For example, if we scale by $2$ the vector $\\mathbf{c} = \\left[ \\begin{array}{c} 2 \\\\ 1 \\end{array} \\right]$, it looks like this:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# vector scaling\n", "c = numpy.array((2,1))\n", "vectors = [c, 2*c]\n", "plot_vector(vectors)\n", "pyplot.title(\"Scaling of the vector $(2,1)$ by the scalar $2$.\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The head of the vector $2\\mathbf{c}$ ends up at the coordinates resulting from scaling the tail-to-head horizontal and vertical distances of $\\mathbf{c}$:\n", "\n", "$$\n", " 2\\cdot\\left[ \\begin{array}{c} 2 \\\\ 1 \\end{array} \\right] =\n", " \\left[ \\begin{array}{c} 2\\cdot 2 \\\\ 2\\cdot 1 \\end{array} \\right]\n", "$$\n", "\n", "##### Exercise:\n", "\n", "_What is the effect of multiplying a vector by a negative scalar?_ Try it! Multiply the vector $\\mathbf{c}$ by a negative scalar and visualize both vectors using our `plot_vector()` function." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Basis vectors\n", "\n", "With the ideas of vector addition and multiplication by a scalar fresh in your mind, now imagine this. Any horizontal vector (i.e., having zero as its second component) can be scaled to have length $1$. \n", "\n", "For example, the vector $\\,\\mathbf{u} = \\left[ \\begin{array}{c} u \\\\ 0 \\end{array} \\right]$ scaled by $1/u$ becomes $\\left[ \\begin{array}{c} 1 \\\\ 0 \\end{array} \\right]$.\n", "\n", "Similarly, any vertical vector (having zero as its first component) can be scaled to have length $1$.\n", "\n", "Going the opposite way, \n", "- scaling the vector $\\,\\mathbf{i}=\\left[ \\begin{array}{c} 1 \\\\ 0 \\end{array} \\right]$ can give us all possible horizontal vectors, and \n", "- scaling the vector $\\,\\mathbf{j}=\\left[ \\begin{array}{c} 0 \\\\ 1 \\end{array} \\right]$ can give us all possible vertical vectors. \n", "\n", "Since every vector is the sum of a horizontal and a vertical one, it means we can generate *all vectors* by adding scaled versions of $\\mathbf{i}$ and $\\mathbf{j}$. That's why they are called **basis vectors**.\n", "\n", "For any vector, its components are the scalars we need to multiply the basis vectors by to generate it. For example:\n", "\n", "$$\n", " \\left[ \\begin{array}{c} 3 \\\\ 2 \\end{array} \\right] =\n", " 3\\cdot\\left[ \\begin{array}{c} 1 \\\\ 0 \\end{array} \\right] +\n", " 2\\cdot\\left[ \\begin{array}{c} 0 \\\\ 1 \\end{array} \\right] =\n", " 3\\,\\mathbf{i} + 2\\,\\mathbf{j}\n", "$$\n", "\n", "Let's visualize this using our helper function." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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dO3d6qiYpPus6++yzNXjwYL377rtasGBB2I8rLCxscX5ZWVkwgLOzs5WdnR1RXbESj/swlrxcF+wiXGMgMTFRqampnjrN4sWapI5fV21trTp37nzEtP79+2vPnj0RbVNOTk6L89PS0oJ/p6SkeKq/Ovo+bG9erQt2eee8BNABDRs27KhppaWl6tGjhwvVAPAKwhWIQkFBgdavXx+8/8orr2jXrl26/vrrXawKgNs4LQxE4cknn9TChQu1aNEi+Xw+GWP0+uuv6/zzz3e7NAAuIlyBKNxyyy265ZZb3C4DgMdwWhgAAMsIVwAALCNcAQCwjHAFAMAywhUAAMsIVwAALCNcAQCwjHAFAMAywhUAAMsIVwAALCNcAQCwjHAFAMAywhUAAMsIVwAALCNcAQCwjHAFAMAywhUAAMsIVwAALCNcAQCwjHAFAMAywhUAAMsIVwAALCNcAQCwjHAFAMAywhUAAMsIVwAALEtyuwCgo1uzZo2WL18un8+n8vJynXrqqVq8eLH69OnjdmkAXMLIFYjS1KlTNXfuXL399tv64IMPlJ6erosvvlgHDx50uzQALiFcgShNnDhR48aNkyQlJCTo5ptvVlFRkbZs2eJyZQDcwmlhIEpr16494n6XLl0kSbW1tWG3UVJS0uL80tLSyAsD4BrCNQZ8Pp+qqqrcLiOoqqrKczVJ8VvXxo0bdfLJJ+vMM89URUVFWI/JysoKu/3q6uqw2421eN2HseLlutLT090uI64QrjFQU1OjgoICJSR446x7fX2952qS4rOu2tpa/cd//IduvPFGbd++PSb1FRUVqby8PCZtRyoe96FttXU+5X9Spk279umcvpkadmo3T9QVqr6+XpmZmW6XEVcI1xhITk7WwIEDlZqa6nYpkvzvSnfu3OmpmqT4rGvmzJm65pprNHv27IgeV1hY2OL80tJSjRkzRpKUnZ2t7OzsiNqPlXjchzbs/6ZSf9xcoDc/KNDbW3ep+lCt/m38eZrxw3Ge7S/YRbjGQGJiolJTUz11msWLNUnxVde8efOUnJysxYsXyxgT0fpycnJanP/PL789DZySkuKp/oqnfRiNXXvL9Pqmj/T6po+0aef/qL7eCc4bPXSAnpk9VQdrajzbX7CLcAUsePjhh1VcXKxf//rXMsYoPz9fkjR8+HAr7W/Ib3lkC/d8tv+Arrh7mT78e3GT8/v2+K7W3nujOiUliS9nHTu8c9If6KCeffZZrVq1SrNmzdKWLVu0efNmrVu3Th9//LG1dfwpJFx9vnpr7SJ6PU78jt546BaN/97go+Ydn9pF6x68Wd27prlQGdzEyBWIQkVFhW666SbV19frvPPOO2Leiy++aGUdn39drq1Fe4P3t3+yT4MGDbTSNqJX5/PpuTfePersQkKC0eq7f6LTTzvZpcrgJsIViEJ6erp8Pl9M1/HmBzsk59vP7zZu261rL7swputEeHZ8uk/TF72k/N3/kCT1yuyu4rIvJUmLb5yk8d87w83y4CJOCwMet27TR0fcz9te5FIlaFDn82nhK+s1bMaCYLDedHmuPn7hXp3YNU3TLz5PP79qrMtVwk2MXAEPO1R7WG9tLjhiWlHJ5you269emSe6VNWxrfFotffJJ2rF7dM0eqj/iu+pF35Pi37yw4ivGEd8YeQKeFjett2qrDl01PR1m2LzAxVoXnOj1e0r7gkGqyQ9+tOrdFznTm6VCY9g5Ap42Pr3P9ZVo4brwJdf6E/v+6dNHn223tpcoFt+OMbd4o4hrY1WQ3npl5fgHsIV8LB/nzpemd266icLnglOu3faJTrhpB4uVnXsqPP59PD/+4PuW/mGDtf5L1y76fJcLZrxQ6Uld3G5OngZ4Qp4WGa3rk1Oz+h2fDtXcuyJZLQKNEa4AkAIRquwgXAFgABGq7CFcAVwzGO0CtsIVwDHNEariAXCFcAxidEqYolwBXDMYbSKWCNcARwzGK2ivRCuAI4JjFbRnghXAHGN0SrcQLgCiFsF/yjVTU+tZbSKdke4Aog7dT6fXnl3h17+y38yWoUrCFcAcWXHp/s07cEV2rqnRBKjVbiDcAUQF5r6bPUnl/xAj918DaNVtDvCFUCH1/hK4F4Z3XTrRUP140mXEKxwBeEKoMNq7krgO68dp10FO1yuDscywhVAh9TS91YrKipcrg7HOsIVQIfC91bRERCuADoMfmUJHQXhCsDzGK2io0lwuwAgHtTW1uqOO+5QUlKSiouL3S4nruz4dJ/O/dki3bXiNR2u86n3ySfqncdm6+lZUwhWeBYjVyBKxcXFuvbaa9W/f3/5fD63y4kbjFbRkRGuQJQqKyu1atUqlZSU6OWXX3a7nLjAZ6vo6AhXIEqDBw+WJJWUlLhcScfHaBXxgnAFPKC1YK6qrmynStzDaBXxhHCNAZ/Pp6qqKrfLCKqqqvJcTVL81VVdXS3Jf5o40h8xyMrKanmB04YesR6v/EiCjX1Y5/Pp8d9s1KLVbx3xm8D3Xf8vSks+rk3bGm/HVqxVVVUpPT3d7TLiCuEaAzU1NSooKFBCgjcuxq6vr/dcTVL81bV7925J0o4dO7R///5YlaeioiKVl5fHrP1IRLsPP/38gBb97n3tLv1KknTyd1J1+4RzNbR3RlQ/Xxhvx1as1dfXKzMz0+0y4grhGgPJyckaOHCgUlNT3S5Fkv9d6c6dOz1VkxR/dTWMXAcPHqzTTjstonUWFha2OP/O53+r3z62VZKUnZ2t7OzsiNqPlbb2VWujVbfqijUv1wW7CNcYSExMVGpqqqdOs3ixJim+6kpJSZEkpaWlRbw9OTktf6540Pl2lJOSkuKp/oq0r9rrs9V4OrbQ8RCuQAewt+xLt0uIGlcC41hCuAJRqq2t1bhx43TgwAFJ0uTJk5WVlaW1a9daW8fez78N15raw9babS9cCYxjDeEKRKlz587Ky8uLWfu79papvOpg8P77BZ9q6JlnxGx9NjFaxbGKcAU87o33tx9xf+O23frpZJeKiQCjVRzLCFfA49ZtOjJc8z4qUn19vae+yhGK0SpAuAKe9nVFlf768Z4jpn1xoEJbi/6p4QMi+7pPe2C0CvgRroCH/f6DHfLV1x81fd17H3kqXOt8Pi18ZT2jVSCAcAU8bNuef2rprCl6+j/XqfB9/7THfnaltpV456s5n35+QLNvX6Kte/y/j8xoFSBcAU9bNOOHSkhI0DNr1genjT9nkGZd19/FqvzqfD4tXrNBD/36j6oLjK4ZrQJ+hCvgYc1dtOT2xUyNP1vtldFNL/xiOqNVIIBwBRC2pq4EvvycbC2b+686+aQTXa4O8A7CFUBYmroS+KmbrlLq4W+s/Ng+EE8IVwAtaul7q07dYeXn57tcIeA9hCuAZrX2vdWKio73O8dAeyBcARyFX1kCokO4AjgCv7IERI9wBSCJ0SpgE+EKgNEqYBnhChzDGK0CsUG4AscoRqtA7BCuwDGG0SoQe4QrcAxhtAq0D8IVOAYwWgXaF+EKxDlGq0D7I1yBOMVoFXAP4QrEIUargLsIVyCOMFoFvIFwBeIEo1XAOwhXoINjtAp4D+EKWPDqq69q4cKFSk5OVkJCgpYtW6ZBgwbFfL2MVgFvIlyBKH344YeaNm2aNm/erAEDBujll1/WRRddpMLCQqWnp8dknYxWAW9LcLsAoKN7+OGHdckll2jAgAGSpKlTp6qurk4rV66MyfqKSj7XuT9bpLtWvKbDdT71PvlEvfPYbD09a4q1YJ2zbK0e+c+3tGtvmZX24tmHhZ9qxiOrtG7TR6o+eMjtcuARhCsQpbffflvnnHNO8H5CQoKGDx+uDRs2xGR9P7zv+eBp4Jsuz9X2FfdYPw2cO6S/bn/2v5Rz/T3q/6O7NGfZWm3c+ncdrquzup54cE5OL+Xv/ocm3LlU3SfO1qV3PKVfvv5n7fvia7dLg4s4LWyRMSZJUuaaNWu0b98+paWluV2SJKmyslJffPGFp2qS4qOur7/+Wt988406d+6skpKS4PT09HR99NFHR0xrSWlpaYvzqw58Gfy7rqpCiSmOuqenat3GTVq3cVNY64iEI0kHKyVJRXsq9dieT/TYqleVlJSozG7H6+TuXZV5QlcZOfr66691wrr3lZTknZeTurq6dq3rUOUB6WClDh6U1ue9p/V570mSBvfuqQvPPl0XDD9dZ/Tuqerqas8e86effvopksocx+EdlAXGcRy3a4gbxphTJP3T7ToAoI2yHMcJ7x0hWsRpYbsy3S4AAKLAa5gl3jmPEx++kKTMzEytXLlSp556qtv16IsvvtDVV18tSZ6pSYqvukaMGKGZM2fqhhtuCE678cYblZSUpKVLl4a13rKyli8c2r17t2688UZJ0iuvvKLhw4eH1W5bbdy2Wz97crUkqdfJ3TX6rGzlntVfQ/tlqVNSoqT42ofRcBxHk+5froLiUh3XOUnfH9hHo8/K1qiz+ivjhG+vFvd6fwWOwS/crideEK52+ST/C+Wpp56qnBz3v2uYlpYWfOH2Sk1SfNU1duxY7d27N7is4zjavXu37rzzzrC3q7XlUlNTg3/37Nkz5v21fOPHeuTn03XZ989S/6yMJpeJp30YjQ8LP9X5Zw/Rolum6YJhOUrpcpwn6gpXaF0KvIYheoQrEKV58+Zp7Nix2r17t/r3769f/epXSkxM1PXXX+92aW32yE+vcruEDmPE6b014vTebpcBjyFcgSiNGDFCK1eu1JQpU4K/0PTHP/4xZj8gAcD7CFfAgiuuuEJXXHGF22UA8AiuFgYAwDLCFQAAywhXAAAsI1wBALCMC5osCvxsmMnLy3N69uzpdjmSpFNOOUXl5eXKz8+XV2qSqCtSJ598cvDvzExv/IiOV/uKuiLTUFd6erpxu5Z4wsgVAADLCFcAACwjXAEAsIxwBQDAMsIVAADLCFcAACwjXAEAsIxwBQDAMsK1HdTX12vEiBHq1auX26Xo0KFDuvfeezVq1CiNHTtWQ4cO1RVXXKFPPvnEtZq++uorzZ8/X+eff75yc3M1ZMgQLViwQHV1da7VFKqoqEjnnXeecnNzXavh97//ffDvH/3oR9q5c6drtYSqra3V888/rxNOOEHFxcVulyNJWrNmjSZOnKjZs2dr1KhRuvLKK109vl977TVdeumluvDCCzVu3DjNmDFDv/3tb12rpznGmFuMMY4xJtftWuIBv9DUDpYuXaqioiJ17drV7VL09ddf6/nnn9fWrVuVkZGh+vp6TZ48Wddcc43+9re/uVLTW2+9pbVr12rTpk3q2rWrPvvsMw0bNky1tbW6//77XampwapVq7Rs2TIlJia6VsOHH36o2267LXj/yiuv1EUXXaTCwkJX/8/Y4uJiXX311TrhhBPk8/lcq6OxqVOnas2aNfrOd76joUOHatasWbr44ou1fft2denSpd3reeaZZzRlyhRNmzZNFRUVeuqpp3TDDTdo2LBhOuOMM9q9nqaUlpZK0ly364gnjFxjbN++fVqxYoVmzJjhdimSpG7dumn9+vXKyMiQJCUkJGjkyJHavXu3qzXNmTMn+OajR48emjRpklavXu1aTQ26d++uP//5z+rXr59rNTz88MMaM2ZM8P6ECRNUV1enlStXulaTJFVWVuq5557T+PHjXa2jsYkTJ+qCCy6Q5D++b775ZhUVFWnLli2u1LNw4UJNmTIleH/IkCGqr6/Xnj17XKmnKbfffrskPeR2HfGEcI2xW2+9VQ899JCSk5PdLkWS1LlzZw0dOjR4f9++fVq5cqVmzZrlWk3jxo3TDTfccMS0Ll26qLa21qWKvnXJJZeoc+fOrtbw9ttv66yzzgreT0hI0PDhw7VhwwYXq5IGDx6svn37ulpDU9auXXvE/YbRqlvH0/Dhw5WU5D9JePjwYa1evVo5OTm68MILXamnsXXr1jXU9we3a4knhGsMNRy0XntnL/lDdfjw4erbt68uuugi10+/Nvbee+/pqquucrsM13355Zf65ptvdNJJJx0xPTMz09XPETuS9957Tz169NAPfvADV+u46aab1KdPH23ZskWvvvqq0tLSXK1HkqqqqnTnnXdq0aJFbpcSdwjXGKmsrNS///u/64knnnC7lCb17NlT+fn5+uS+ZmMAAAAN5klEQVSTT/TWW2/pJz/5idslBb3zzjvau3ev7rrrLrdLcV11dbUkHTV6Pu6444Lz0LxDhw5p8eLFWrJkiTp16uRqLUuXLlVxcbGGDRumcePGNXzO6aq7775bM2fO9Mz/tBRPCNcIGWPmB66oa/a2a9cuLViwQDNnzjzivwqLpfnz58sY0+Tt+OOP1+jRo5v8zKlHjx566KGHtHz5cutXoLZUU0Ndu3btOuIx+/bt08yZM/Xaa6/F7AKwttTllpSUFElHn9I8dOhQcB6aN2vWLE2aNElXXnml26VIkhITEzV9+nQ5jqPHHnvM1Vq2bt2qDz74QDNnznS1jnjF1cKRe0TSsy0t0K9fv9Knn35aH3/8cfDzn+LiYpWVlSk3N1f9+vXT8uXLrRY1d+7cZp8klZWV2r59u84888zgVZ2hV78OGDBAklRQUKBBgwa1S00Ndf3jH/8I3v/qq680YcIELVu2TMOGDbNWR7R1ual79+7q2rWrPv/88yOml5WVqU+fPi5V1TE899xz6tSpkxYuXOhqHbW1tUeceUhISFDfvn1VUFDgYlXSG2+8oZqaGo0ZM6bhdaHhCsInjDEHJP3YcRzvXHXVwRCuEXIcp1JSZUvL5OXladOmTUd8TWL+/Pl66aWXlJeXF5O60tLSmv0Mp6KiQt26dVNSUpJWrVql/fv3a+7cb6+6bzg91aNHj3arqaGukpKS4N+XXXaZ7rnnHo0dO1aS/8UxFldZR1KXF4wZM0bbt28P3nccR1u2bNGdd97pYlXe9vjjj6usrEyvvvqqjDHKz8+X5L+4qL0NGzZMO3bsOGJaWVmZRo4c2e61hLr77rt19913S/If88cff/xkSZ9Kus1xnDw3a4sHnBY+Br3wwgvav3+/JOngwYN64IEHNHjwYJ1zzjmu1HPw4EFNmDBB5557rnr27KnNmzdr8+bN+uUvf+lKPV4zb948vfPOO8H769atU2Jioq6//noXq/KuZ599VqtXr9aVV16pbdu2afPmzVq3bp0+/vhjV+opKCjQ+vXrg/f/9Kc/qaioiP0X7xzH4Wb5tnHjRqe8vNxxHMcpLS11Ro0a5Zx22mnOcccd54waNcp58cUXnfZUXl7uNNS0d+9e5+abb3aGDh3qjBw50hk6dKgzdepUZ+/eve1aU2hdjzzyiCOpyZsbQvvrtddec0aNGuVkZGQ4Xbt2dUaNGuUsX7683Wt67rnngn1y9tlnOzt27Gj3Gho7dOiQc/755zt9+/Z1JDnf+973nEmTJrlaU3l5uZOQkNDksdTez7sGS5Yscb7//e87559/vjNixAhn0KBBzpo1a1yppTk//elPHUnvB/pqm6TVjgdeSzvyzTiO0955Hvfy8vKc4cOHu/rrOaEqKiqUn58vL9UkUVckSkpKlJWVJUkqLCxUTk6OyxX5ebGvJOqKVEVFhdLT043bdcQTTgsDAGAZ4QpEyQs/7A/AWwhXIAqrVq3StGnTlJDAUwnAt3hFAKLghR/2B+A9fM8ViMIll1xipZ3WvlfrhZ/KAxA+wjUGfD6fqqqq3C4jqKqqynM1SfFV1+HDh+Xz+VRRUdGmdTZcCRyO6urqNq/Htnjah+3By3V56erleEC4xkBNTY0KCgo88zlcfX2952qS4quuL7/8Mvg1i1grKipSeXl5zNcTjnjah+3By3Xx4/12Ea4xkJycrIEDByo1NdXtUiT535Xu3LnTUzVJ3q3rvvvu06OPPtriMnl5eUf8/nH37t1VVVXV5p/XKywsbHF+WVmZRo8eLUnKzs5WdnZ2m9Zjm1f3IXVFxmsj6XhAuMZAYmKiUlNTPXWaxYs1Sd6sa86cOTrvvPN05plnNvsbxCeeeGLwP8CWpE6dOikxMbHN29Haj0KE1pGSkuKp/vLiPpSoC+4iXIFG0tLS1K1bN2VkZPACCKBNvHPSHwCAOEG4AlF4/fXXlZubqz/84Q/atm2bcnNztWLFCrfLAuAyTgsDUZgwYYImTJjgdhkAPIaRKwAAlhGuAABYRrgCAGAZ4QoAgGWEKwAAlhGuAABYRrgCAGAZ4QoAgGWEKwAAlhGuAABYRrgCAGAZ4QoAgGWEKwAAlhGuAABYRrgCAGAZ4QoAgGWEKwAAlhGuAABYRrgCAGAZ4QoAgGWEKwAAlhGuAABYRrgCAGAZ4QoAgGWEKwAAlhGuAABYluR2AUBH9dVXX2nJkiXasGGDkpKSdODAAU2aNEnz5s1TUhJPLeBYxisA0EZvvvmm1q5dq02bNqlr16767LPPNGzYMNXW1ur+++93uzwALuK0MNBG3bt315w5c9S1a1dJUo8ePTRp0iStXr3a5coAuI2RK9BG48ePP2paly5dVFtbG3FbJSUlLc4vLS2NuE0A7iFcY8Dn86mqqsrtMoKqqqo8V5MUn3X99a9/1cSJE1VRURHR47KyssJetrq6OuL2YyUe92Esebmu9PR0t8uIK4RrDNTU1KigoEAJCd44615fX++5mqT4q2vLli365JNPdNdddyk/Pz9m9RUVFam8vDxm7Uci3vZhrHm5rszMTLfLiCuEawwkJydr4MCBSk1NdbsUSf53pTt37vRUTZJ367rvvvv06KOPtrhMXl6ehg0bFrz/2WefadmyZfrNb36jIUOGRLzOwsLCFueXlZVp9OjRkqTs7GxlZ2dHvI5Y8Oo+pK7IeG0kHQ8I1xhITExUamqqp06zeLEmyZt1zZkzR+edd57OPPNMpaWlNbnMiSeeGPy6zVdffaUpU6bo2Wef1ciRI9u0zpycnBbnh9aRkpLiqf7y4j6UqAvuIlyBRtLS0tStWzdlZGS0+gJYUVGhyy67TPfcc4/Gjh0rSXruuec0Y8aM9igVgEd556Q/0MEcPHhQEyZM0LnnnquePXtq8+bN2rx5s375y1+6XRoAlzFyBdpoxYoVysvLU15enh577DG3ywHgIYxcgTa66aab5DhOkzcAxzbCFQAAywhXAAAsI1wBALCMcAUAwDLCFQAAywhXAAAsI1wBALCMcAUAwDLCFQAAywhXAAAsI1wBALCMcAUAwDLCFQAAywhXAAAsI1wBALCMcAUAwDLCFQAAywhXAAAsI1wBALCMcAUAwDLCFQAAywhXAAAsI1wBALCMcAUAwDLCFQAAy5LcLgDoqA4dOqQHH3xQeXl56tSpk7788kv16tVLjz76qPr06eN2eQBcxMgVaKOvv/5azz//vNasWaMNGzYoPz9fnTp10jXXXON2aQBcRrgCbdStWzetX79eGRkZkqSEhASNHDlSu3fvdrkyAG4jXIE26ty5s4YOHRq8v2/fPq1cuVKzZs1ysSoAXsBnrkCU9u3bpwkTJmjnzp2aM2eO7r///ojbKCkpaXF+aWlpW8sD4ALCNQZ8Pp+qqqrcLiOoqqrKczVJ8VPX8ccfr7y8PJWWlmry5Mnat2+fnnrqqYjWmZWVFfay1dXVqqioiKj9WImXfdhevFxXenq622XEFcI1BmpqalRQUKCEBG+cda+vr/dcTZJ363rxxRf18ssvt7jMs88+qwEDBhw1/brrrtPcuXM1atQo9e7dOyb1FRUVqby8PCZtR8qr+5C6IlNfX6/MzEy3y4grhGsMJCcna+DAgUpNTXW7FEn+d6U7d+70VE2Sd+vKysrSpZdeqgEDBiglJaXJZbp37y5jjCQpMTExOD0jI0Nz585VYmKihg8fHvY6CwsLW5xfVlam0aNHS5Kys7OVnZ0ddtux5NV9SF2R8dpIOh4QrjGQmJio1NRUT51m8WJNknfr+u53v6vevXu3WNdLL72k/fv3a+7cucFpDadr+/btG9E25eTktDg/LS0t+HdKSoqn+sur+5C64CbvnJcAOqAXXnhB+/fvlyQdPHhQDzzwgAYPHqxzzjnH5coAuImRK9BGF1xwgfLz8zVu3DilpaWpsrJSgwYN0ptvvqnOnTu7XR4AFxGuQBtlZWVFfFUwgGMDp4UBALCMcAUAwDLCFQAAywhXAAAsI1wBALCMcAUAwDLCFQAAywhXAAAsI1wBALCMcAUAwDLCFQAAywhXAAAsI1wBALCMcAUAwDLCFQAAywhXAAAsI1wBALCMcAUAwDLCFQAAywhXAAAsI1wBALCMcAUAwDLCFQAAywhXAAAsI1wBALCMcAUAwDLCFbCgvr5eI0aMUK9evdwuBYAHEK6ABUuXLlVRUZHbZQDwCMIViNK+ffu0YsUKzZgxw+1SAHgE4QpE6dZbb9VDDz2k5ORkt0sB4BFJbhcAdGTr1q1TUlKSxo8frw8++KDN7ZSUlLQ4v7S0tM1tA2h/hGsM+Hw+VVVVuV1GUFVVledqkjp+XZWVlZo3b55+97vfqaKiQocOHZLjOKqoqIh4nVlZWWEvW11d3aZ1xEJH34ftzct1paenu11GXDGO47hdA+Apxpj5ku5tZbFzJF0naY/jOEtDHjfdcZxebVhnJE/ELMdxWh7qAnAV4Qo0YoxJk5TWymL7JeVL+kZSfWBaL0mZkt6XP3R/HME6T2llkURJ35VUJqnMcZy6cNsG0P4IV8CSaEauAOILVwsDAGAZ4QpEyRiTaYzJkzRdUqYxJs8YM93VogC4itPCAABYxsgVAADLCFcAACwjXAEAsIxwBQDAMsIVAADLCFcAACwjXAEAsIxwBQDAMsIVAADLCFcAACwjXAEAsIxwBQDAMsIVAADLCFcAACwjXAEAsIxwBQDAMsIVAADLCFcAACwjXAEAsIxwBQDAMsIVAADLCFcAACz7/yeD1KFV3uuPAAAAAElFTkSuQmCC\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# basis vector\n", "i = numpy.array((1,0))\n", "j = numpy.array((0,1))\n", "\n", "vec = 3*i + 2*j\n", "vectors = [i, j, 3*i, 2*j, vec]\n", "plot_vector(vectors)\n", "pyplot.title(\"The vector $(3,2)$ as a linear combination of the basis vectors.\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Linear combination and span\n", "\n", "Adding two vectors that were each multiplied by a scalar is called a **linear combination** of those two vectors. Thus, we say that every vector is some linear combination of the basis vectors.\n", "\n", "This brings us to the idea of the **span** of two vectors: the set of all possible linear combinations of the two. The second episode of the series [_\"Essence of Linear Algebra\"_](http://3b1b.co/eola) uses rich visuals to bring these ideas to life [2]. Recommended!\n", "\n", "\n", "In the code cells below, we will use the NumPy function [`randint`](https://docs.scipy.org/doc/numpy-1.15.0/reference/generated/numpy.random.randint.html) to get random integers in an interval (in this case, from $-10$ to $10$). We then create a list of 30 random vectors on the plane via a linear combination of the basis vectors $\\mathbf{i}$ and $\\mathbf{j}$, and we draw them all. " ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "from numpy.random import randint" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# span\n", "vectors = []\n", "i = numpy.array((1,0))\n", "j = numpy.array((0,1))\n", "\n", "for _ in range(30):\n", " m = randint(-10,10)\n", " n = randint(-10,10)\n", " vectors.append(m*i + n*j)\n", " \n", "plot_vector(vectors)\n", "pyplot.title(\"Thirty random vectors, created from the basis vectors\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can imagine that if we created more and more random vectors in this way, eventually we will fill up the 2D plane. Indeed, the *span* of the basis vectors is the whole 2D space. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "What if we tried the same experiment, but making linear combinations of the vectors $\\mathbf{a}$ and $\\mathbf{b}$, defined above?" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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HJCZRMJLkhShCw4YN43//+5/hS/DixYvUrVuXjz76yNC02apVK44cOcLAgQMBXcI/d+4cCxcutFXYQogSwj5O7gjxAHv77bdZt24d0dHRACxbtoymTZvSu3dvG0cmhCju5EheiPtk4sSJHDp0yPDax8eH7777jv79+3Pjxg169uyJi4sL5cuXZ9u2bXZzgZUQoviSJC/EffLRRx9ZHDd69GhGjx59H6MRQjwI5FBBCCGEKKEkyQshhBAllCR5IYQQooSSJC+EEEKUUJLkhRBCiBJKkrwQQghRQkmSF0IIIUooSfJCCCFECSVJXgghhCihJMkLIYQQJZQkeSGEEKKEkiQvhBBClFCS5IUQQogSSpK8EEIIUUJJkhd2S1VVVFW1dRhCCFFsSZIXdm3ht7tIS8+wdRhCCFEsSZIXdktRFKLvJNBl0hKibsfZOhwhhCh2JMkLu/bUwy3589R/tBn9HkfPXbJ1OEIIUaxIkhd27aHG9fEs58GV6Bg6jf+A7/YE2TokIYQoNiTJC7vm4KDh8Q4tAEhOTeeZeZ8zY/VmMjO1No5MCCHsnyR5Yfee7NTS5P2Cb3bxxNsriEtMtlFEQghRPEiSF3ava2sf3FxKmQzbfugk7ccsIOxKlI2iEkII+ydJXti90qWc6dW2icmwimXcaFG/BlsOHpemeyGEsECSvCgWsjfZJ6akMXt4P6Y83RMHB6nGQghhjnw7imKhT/tmODpomDykBzU8y5OSls7wBV+SkZlp69CEEMJuSZIXxUJ5Dzee796eOSP68cWUYQAcPnOBxd//ZuPI8rZ9+3b69u1L9+7d6dSpE35+fmzcuNFkGlVVmTt3Lq1bt6Zt27YMHTqU2NhYG0UshCgpJMmLYmPl68/h6lKKHv5NeKXfIwDMWruNUxeu2jiy3H3++ecMHjyY33//nYMHDzJ79myeeeYZTp48aZhm6dKlbNy4kYMHDxIUFISzszPDhg2zYdRCiJJAkrwoNko5OxleLxo9kDpVKpKWnsGw+WtIz7DfZvuZM2fy7LPPGt4HBASg1Wo5f/48AJmZmSxYsIAxY8bg6uoKwOTJk9m6dSunTp2yScxCiJLB0dYBCFEQHq4urJ02goDXl3AsLILFmwLp0bCSrcMyq1WrVjg66na19PR0Fi1aROPGjenevTsAJ06cIDo6Gn9/f8NnfH19cXNzIzAwkKZNm1q1nCtXruQ6/vr16wVcAyFEcSVJ3k7Fx8cDkJiYSGZmJomJiTaO6C57ial1/Wq82u9hVm47wKKNgdQa0RUfH/stp0mTJrFp0yZ8fHz48ccfUVWV+Ph4QkJCAHB3dzdsdwBPT09CQ0NNhuWmZs2aVseWlJRk9XyLmr3Upyz2Fg8Un5g8PDxsGJEwR5K8nQoODgZAq9WSnJzM6dOn0Wjs4+yKPcX0eLOqbPvTgyu345m/5RB1KpfDxahZ35ayl9Nzzz3H008/zbp16wgICGDFihVUrFiR06dPAxAaGkpkZKTh86qqEhERYagLhSksLIy4OPt4sp891Sd7jAeKT0wBAQG2DUrkIEneTvn5+QG6X8shISE0btwYNzc3G0elY28xfVnOi57TPubyrXi2h0Ty/qgnbR0SYLmc2rRpQ9OmTfnjjz949913Dc3sPj4+VK9e3TCdoijUrFnTUBfycubMmVzHR0ZG0rlzZwC8vb3x9vbO7yoVCXurT/YWD0hMouAkydsp42YvBwcH3Nzc7KopzJ5i6ubfjPFPBfDR5r188stBnuvZkfaN69k6LEBXTk5OTjnKqWHDhpw/fx4PDw+aNNH15peQkGCYTlVVoqOj8fHxsbqMfXx8ch3v7u5ueO3q6moX2y6LPdUnsL94QGISBWMf7T5C3KM3n+1Jbc+yaLUqIxZ8SXJqmq1DMnj44YdzDLt+/TrVqlUDoHnz5nh6enLkyBHD+NDQUBITE+nWrdt9i1MIUfJIkhclgouzEzOefAgHjYazEVG89fkWW4dkEBoayvbt2w3vv/rqK86ePcvw4cMB3dHQ9OnTWbFiBUlJSQAsWbKEfv36WX1lvRBCmCPN9aLEaFStApMHd2Xhd7/z0Y+7ebJTSx5p0dDWYbFw4ULee+89FixYQGZmJoqisHXrVjp16mSY5vXXXychIYGOHTvi5OSEt7c369evt2HUQoiSQJK8KFGmDOrGr0dCOX4+ghEL13Lii5m4l3axaUyjR49mypQpuU6jKAozZ85k5syZ9ykqIcSDQJrrRbG17a9/OX/1hskwZydH1s8YiZOjAxeu32Tqqh9tFN29+f3IaXmErhDinkmSF8VW49pV8XvlXb7dHWQyvFm9Gswe3g+AlVv3Exh82hbh3ZPA4DN89fshW4chhCjmJMmLYqt+9co0q1udZ9/9nHEfbyQlPcMwbuozPWnrUweAFz5YR2xCko2iLJjoO/G8veZnu7pLQAhR/EiSF8XasB4PAbDut8O8uvpXzlzW9Rjn6ODAuhkjcXF2IuJGDJM+2WTLMPMtOjaBK9ExfPTDbluHIoQoxiTJi2JtUIAfpZx0149ejI4lYNJHrP7lAKqq4lOrKu+9qOv9bs3OP/nl7xO2DDVfbsYmADD/m51E37GPPuaFEMWPJHlRrJX3cOPxDi0M75PT0nl5yQaembeauMRkJgzoSqdmDQB4afF6bsfZzwM+cpOV2OOTUpi3fnseUwshhHmS5EWxN6znQzmGfb/3CK1ensex85dZO20Eri7ORN6OY9yyb20QYf5Fx949el+5dR9hV6JsGI0QoriSJC+KvZ7+jalU1t1kWEDLhix8eQAVPNyoX70yH7w8AIBvdgex+Y+jtgjTamnpGcQlphjeZ2RqmbH6JxtGJIQoriTJi2LPydGRgY+0MhkWfO4yLRvUpF41TwBefeJRurbWPcBl9NKv7fo8d9b5eGM//nGUv0P+s0E0QojiTJK8KBGe6ax7HOuXU4biVb4M8UkpDJ7zKSlp6QBoNBrWTB2Oh6sL0XfiGf3hV6iqasuQLcqe5J2dHHEvXYrJK3+w25iFEPZJkrwoEVrWr8FT/g0Z8HArvn7rRRRF4VhYBG8Y3TpXy6siS18bDMDmA8dydKJjL6LvxOPi7MSzXdsC4KBRuPHTEpa8Noi4xGQbRyeEKE4kyYsSQVEUxvRqDUBXP19mDusDwCc/72Pj3ruPcH2hd0d6t9M92W3ssm+5dvPO/Q82Dy7OTvz18TTe1d/+l5yaTujlSNo3rkdZd1cbRyeEKE4kyYsSw0Fztzq/83xfOrdqBMCoxesNfdwrisLqycMo5+5KTHwSLy/ZYHdN4B2bNaCVdy3qVKmIZzkPAA6fuWDjqIQQxZEkeVEiOTho+ObtUWbPz1erVI7l458GYPuhk6zd9ZctQ7VIURTa+dYFJMkLIQpGkrwosapUKGvx/Pxz3drx1MO6K/Inrviey1G3bBVmrrL63w+SJC+EKABJ8qJEs3R+XlEUVr3+HJXKuhOXmMKLi9bbXbM9YDiSP3M5Ui66E0LkmyR5UeJZOj9fuXwZVr7+HKB7tOuqrfttFqMlbfVJXlVV/gm9aNtghBDFjiR5UeLldn5+4KN+PN3FH4Apq34k/Fq0LUPNoZy7K41qegFyXl4IkX+S5MUDIbfz8x+Pf4YqFcqQmJLKyIVr0Wq1Now0p3a+9QBJ8kKI/JMkLx4Yls7PVyzrzmdvPA/AHyfCWLZ5j81iNMf4Cnt7vG5ACGG/JMmLB4ql8/P9OrRgRK8OAMxY/RNnL0faLMbsspJ8VEwcl6Nu2zgaIURxIklePFByOz//0ZjB1PAsT0paOsMXfElGZqaNo9VpVq86pZwcAQgKlSZ7IYT1JMmLB46l8/Nl3V35YsowQNc0vvj732wZpoGzkyOtG9YC5Ly8ECJ/JMmLB5Kl8/M9/JvwSr9HAJi1dhunLly1WYzGpOc7IURBSJIXDyxL5+cXjR5InSoVSUvPYNj8NaRnZNgyTOBukg8+d8ku4hFCFA+S5MUDy9L5eQ9XF9ZOGwHAsbAI3v965z0va+PGjfTo0YOuXbvi7+/PgAEDCA8PN4xXVZW5c+fSunVr2rZty9ChQ4mNjTWMz7qNLjk1nVMXrt1zPEKIB4MkefFAs3R+/tGWjZgwoCsA727YztFzl+5pOUOHDmXy5Mns3r2bw4cP4+HhQa9evUhJSQFg6dKlbNy4kYMHDxIUFISzszPDhg0zfF6eSCeEKAhJ8uKBZ+n8/PujnsS7RmUyMrUMm/8lqfqr8AviiSeeoEePHgBoNBrGjh1LWFgYR48eJTMzkwULFjBmzBhcXXXPi588eTJbt27l1KlTgDyRTghRMJLkhcD8+XlXl1Ksmz4SjUYh5OI1Zq/bVuD5b9q0yeS9i4sLAGlpaZw4cYLo6Gj8/f0N4319fXFzcyMwMNAwLOuJdJaS/JUrV3L9u379eoHjF0IUT462DkCYFx8fD0BiYiKZmZkkJibaOKK7SmpMn018mo4TPuTGnXgGzlzJ7x+Mo2mtyox/MoCPNu/lg+9+pVvLhrT1qX3PMe3du5eqVavSvHlzduzYAYC7u7thuwN4enoSGhpqGNasThUAQi9HciXyBmXdSpvMs2bNmlava1JSksmybMne6pO9xQPFJyYPDw8bRiTMkSRvp4KDgwHQarUkJydz+vRpNBr7aHgpyTFN7efPlA17+Df8Ki8t+IKJffx5zLcyP3mW5VJ0LCMXrmX1K70MndMUJKa0tDQ++OADXnnlFU6cOMHp06cBCA0NJTLybk97qqoSERFhqAuOKWmG4d/v2INfvSoFXs+wsDDi4uIK/PnCZG/1yd7igeITU0BAgG2DEjlIkrdTfn5+gO7XckhICI0bN8bNzc3GUemU5Jj8/OBmuiMLvvuNn4+E8VSX9vTv5Mf6ilXpMnkZEbfi2BYSyfwXnyhwTKNHj2bIkCFMmjQJ0DWzA/j4+FC9enXDdIqiULNmTUNdAPCuvp+wq9HEqaVMhgOcOXMm13giIyPp3Lmzbj7e3nh7e+e5DveDvdUne4sHJCZRcJLk7ZRxs5eDgwNubm521RRWkmN6d1R/Dp+9xN5jZxn38SY6Nm/EI60a89bQ3sxd/wufbD3A4M5teaRFw3zHNH36dEqXLs2iRYtQFAWAJk2aAJCQkGCYTlVVoqOj8fHxMVmfh5o0IOxqNMfDr+VYTx8fn1xjcXd3N7x2dXUtkduusNhbPCAxiYKxj3YfIeyIpfvn3xram5YNaqKqKiMWriUhOSVf8124cCEXL17ks88+Q1EUgoODCQ4Opnnz5nh6enLkyBHDtKGhoSQmJtKtWzeTecgT6YQQ+SFJXggzzN0/7+zkyPoZI3FydODC9ZtMXfWj1fNbtWoVGzZsYMKECRw9epQjR46wbds2Tp48iYODA9OnT2fFihUkJSUBsGTJEvr160fTpk1N5iNPpBNC5IckeSEsMHf/fLN6NZg9vB8AK7fuJzD4dJ7ziY+PZ8yYMYSEhNChQwf8/f3x9/dnzpw5hmlef/11Bg0aRMeOHWnbti3JycmsX78+x7ya17/7RDq5X14IkRdJ8uKBp9VqLY4zd//81Gd6Gu5Zf+GDdcQmJOU6fw8PDzIzM1FVNcffiBEjAN1FdjNnzuTYsWMEBQXx9ddfU65cuRzzcnK8+0Q6eeysECIvkuTFAy85NZ3xy74j8nZsjnHmzs9nZGpZN2MkLs5ORNyIYdInm8zMtehIz3dCCGtJkhcPPLfSpahQxpVGw95hxU97ycw0PbI3d37ep1ZV3nvxSQDW7PyTX/4+cd/ilSfSCSGsJUleCGDsU51Jz8hk7LJvaT9mfo4H0pg7Pz9hQFc6NWsAwEuL13M77v70RiZPpBNCWEuSvBBApbIejOr9MABHzl7C/9X3mbD8O+ISkw3TZD8/fyHyJmunjcDVxZnI23GMW/btfYm1aoUyeJbV3fMuTfZCiNxIkhdCb9Lgbjjou+fUalWWbd6Dz/CZbNp3BFVVzZ6fr+5Zng9eHgDAN7uD2PzH0SKP82ZcIhXK6HoYkyQvhMiNJHkh9OpUqcTTXfxNhl2/FcvgOZ/Re/oy/rt6w+z5+VefeJSurXW9zY1e+jXRd4r2wS93EpIIv34TkCQvhMidJHkhjEx9umeOYc3qVaebny9U+T5tAAAgAElEQVSp6bqL3LKfn/9h/1HWTB2Oh6sL0XfiGf3hV0XaG11sQjLpGZmA7ol0ed3CJ4R4cEmSF8JI8/o1eKydaS9zN2Li6f9waxrXqWYYlv38fFpGJktfGwzA5gPH+HZ3UJHFeMcoqauqypGzl3KZ2vZOX7xGfFL+ugAWQhQOSfJCZDNNfzTfq20TyrqVJiomjl7T/sfN2LvN8ObOzz/brS299T8Qxi77luu3ct53XxhijS4GBDh0OrxIllMYwq9F8/S81biXLmXrUIR4IEmSFyKbR1o0pJ1vXRa81J+f5r2Ks5Mj5yKi6PfmCpJSUg3TZT8/P3nlD6yePIxy7q7ExCcxfsWmImm2v5NgmuQ3HzhW6MsoDFejY+g2eSnl3V0NT9wTQtxfkuSFyEZRFNZMHU6LBjXp3MqH9dNHAroj5mfmfU5GZqZh2uzn5w+ePM/y8U8D8OuRM+w6XvhH2dmP5I+fjyA+KdnC1LZxMzae7lM+4sL1mzSrV93W4QjxwJIkL4QZxuffh3TxZ8mrgwDY+te/jFv2nckRevbz8+186/LUw60AWPHrUa5ExxRqbHeyXWinVVXe/HxLoS7jXsQmJNFr6jLOXLoOQNO6kuSFsBVJ8kJYYdLg7rw+UPds91Vb9zP/652GcdnPzw+Z+xkfjR1CxTJuJKamM2bZ94XabJ/9SB7g061/cDHyZqEto6CSUlLp99YKgo16DGwmSV4Im5EkL4SVFr86kMEBbQB464strNv1l2Fc9vPzC7/ZxdJXdZ3k7P03jFVb9xdaHFlH8i7OToZhfo1qs/3vk4W2jIJIS89gwKxVHDgRZjK8Sd1qFj4hhChqkuSFsJJGo2HdjJE82qIhoGua/zUoxDA++/l5rarSpWltAKas+pHwa9GFEkd6RiY/zH6Fpzq1MgxzdNAw5qnOhTL/gsjM1DL0vS/YZVQeADUrl6ecu6uNohJCSJIXIh9cnJ3Y8u5rNKlTjYxMLQNmrSLY6D514/Pz45ZvZFB7H7zKe5CYksrIhWtzfXa9tVZNGsqAR/14uHkDwzBbP5Fuwbc7OXLuEuU9TBO6nI8XwrYkyQuRT+XcXdm5cDzVK5UjMSWVPjOWc0HfzazJ+fnkVD78JYjFrzwFwB8nwli2ec89L9+znAeA4Ql4YPsn0r01tA/h37xPi/o1AAy3zMn5eCFsS5K8EAVQs3IFdi4cTxk3lxyd5Rifnw+LjGH/ifOM6NUBgBmrf+Ls5chCiaFJnWqUcXUxvLd1P/b7jp9l3/FzAHz15gvU9qoot88JYWOS5IUooGb1arBl3mtmO8vp6ufLtCHdAfh8x1882rwhNTzLk5KWzvAFX5rca19QGo3G5Gje1kl+zrptALT1qcMzXduycdbLtGpQy6YxCfGgkyQvxD3IrbOcaUO606qOFwDjP/6OuS88DuiS8eLvfyuU5T/c3Nvw2pZJ3vgofvaIfiiKQlvfunJlvRA2JkleiHtkqbMcBwcNbw/oQOVyHsQnpbB88x5G9e4EwKy12zh14eo9L9v4SN6WT6QzPorv1bZpHlMLIe4XSfJCFAJLneVUcC/N5288a7h/HqBOlYqkpWcwbP6ae74ivk2jOjg5OgC2eyKduaN4IYR9kCQvRCHJ3lnO17v/ASCgRUPD/fOf7zjI8B4PAXAsLIL3jXrOKwgXZyfa+tQxvLdFk70cxQthvyTJC1FIsneWM+7jjQSd193WZnz//Ic/BDK8py7Rv7thO0fP3dvRty3Py8tRvBD2TZK8EIUoe2c5szYe5Nj5CDIzM2ii3IC0JOKTUjh+/jINqlcmI1PLsPlf8vEnK2ndujUdO3akT58+XL1q/fn6Tk3vnpc/dDq8SB5va4kcxQth3yTJC1HIsjrLqVaxLCnpGfSf9RntAroRdzMSTu9FUeDf/67SvF51NBqFkIvXmLZyI7t27eLPP/+kXbt29O3b1+re8To0rW94feNOPJejbhfVqpmQo3gh7J8keSGKQM3KFfhx1ku4lXLiVnwSsbUeov+QZ+DONcY/rrvCfvOBY/Rt3xyA5ErehN9MAGDChAmcOnWKHTt2WLWs8h5uNKlT1fD+fjXZy1G8EPZPkrwQRaRJnarMG/IIzo4OXIiK4c1v94PGgXGPdzKcn9999AwkxaICIxZ8SXJqGmXLlqVhw4YEBgZavayHmzc0vA785wRXrlzJ8Xf9+vVCWzc5iheieHC0dQDCvPh4XRepiYmJZGZmkpiYaOOI7pKYrJOYmEjzWpVY9lp/Ri/bxOkrt6BxF+LjE/hs4tN0nPAhN+7Eg6pFoyicjYhiysqNzH/xCTw9PTl37pyhHuSljXcNw+vV321h9bQXc50+KSnJ6nmbM3PNFgD8Gtaio2/te5qXvW07e4sHik9MHh4eNoxImCNJ3k4FBwcDoNVqSU5O5vTp02g09tHwIjFZJysm77KuvNqjFSt/OwaV6jDls594c+AjTO3nz5QNe1DdylOjnAuXY5L55Oc/8C7vTEpKCvHx8YZ6kBf3TKMvf49KoCiQywV4YWFhxMXFFWi9jl+M4sDJ/wAY1KYeR48eLdB8stjbtrO3eKD4xBQQEGDboEQOkuTtlJ+fH6D7tRwSEkLjxo1xc3OzcVQ6EpN1jGNa6O/P9VtxbAn+j8DTV+kQfofJg/twKiKatftOcjkmmVqVy3P5Rgwf7TxKDZfSVKhQwVAPrOG5JpDouETQOPLjr/toXLOyyfjIyEg6d9Y9c97b2xtvb29zs8nTzM2fALqj+FeH9L3npnp723b2Fg9ITKLgJMnbKeNmLwcHB9zc3OyqKUxiso5xTOP6tGXLzt+gcn3mfrWTetW9WDTmWdb+NBzKV+NmXCJODg5cjLpNbLI7w1rWz9e6dPVrzHd7dR3w3EhW6e/jYzLe3d3d8NrV1bVA5bTv+FnDUfy8F56gTJky+Z6HOfa27ewtHpCYRMHYR7uPEA8AjaJA6H7aNdI9mW3U4vUEh0fS1OEGbk4KSSlpVCqnS8QxrlWp5N0iX/N/pIVRpzinwwsvcCNyRb0QxYskeSHuJ20mn40faOgsZ8CsVQx76VWc//sLRVG4fisWNyfdbvnZH6H5euCM8cNqDpw8X+ihyxX1QhQ/kuSFKGJpaWkEBAQwceJEAF5+YQS1Y09TvVI5ElNSWfJbCJNeHYVXsq6Xu8R0LU4OGiJuxDDpk01WL6dJnWq4ujgDEH4tutCfSCdH8UIUP5LkhShizs7O7Nu3j+PHj6OqKocOHWL75o3sXDieMm4uRMXEseHETY5v/8Zw/3zW1cprdv7JL3+fsGo5Go2Gjk10vd+pwD9nLxbaOshRvBDFkyR5IWykWb0abJn3Gs5OjpyLiOLJdz7h8ynD8CpfhtT0DNz0R+UvLV7P7Tjr7o/u0vruxXZBZy4WWqxyFC9E8SRJXggb6tzKh/XTRwK6h8u8/vFG1k8fiaIoJKak4eigIfJ2HOOWfWvV/IzPy+//91yhxChH8UIUX5LkhbCxIV38WfLqIAC2/vUvP/15nHee7w1ARqbuITXf7A5i8x95dzrTplEdHPRN/YfPXCiUJ9LJUbwQxZckeSHswKTB3Xl9YDcAVm3dj5Ojo+H8fFbSHr30a6Lv5N59rIuzE03rVgMgNjH5np9IJ0fxQhRvkuSFsBOLXx3I4IA2ALyz5mee7NgSr/JlyNRq0WgUou/EM/rDr/I8Ou/h39jw+l6fSCdH8UIUb5LkhbATGo2GdTNG8mgL3RPl3li5iYkDu6IoClqtLrFvPnCMb3cH5TqfR42eSHfgZFiB45GjeCGKP0nyQtgRF2cntrz7mqGznHc37GBUn44m04xd9i3Xbt6xOI8OTesbXu89drbAschRvBDFnyR5IexMOXdXdi4cb+gsZ+ufJ2jfuK5hfEx8Ei8v2WCx2b68hxs1PMsDcDYikvSMjHzHIEfxQpQM8oAa8UD65e8TvP3FFhw0GtxLl8LD1QX30qVwL+2Ch6vuv3vpUri7lMKnVhW6+vne1/hqVq7AzoXj6TT+A6Ji4nAvXQrPsu5ExyYAsP3QSdbu+ouRj3U0+/lHm3vz9e4gMjK1nLpwjVbetfK1/NlrtwJyFC9EcSdJXjyQ+j7UnDpVKvL03NUcDbtscbo6VSqy58M37mNkd2V1ltNr2jL+uxaNb+2qhiQPMHHF93Tz86Vm5Qo5PvtYu6Z8rT93/9ep8/lK8nuPhbL/X925fDmKF6J4k+Z68cBqWrc6QStn8Eq/RyxOM+CR1pQu5XQfozJl3FnOmUvXaVTTyzAuLjGFFz5YZ7bZ/uHmd59ItzMoxOrlqarKsPlfAuBdvbIcxQtRzEmSFw80V5dSrJo0lB9mv0I5d9cc45ds/J3qg6bSffJSvtz5Z74e+pKZqSUqNvGeO6QZ0sWfeSMfB+BsRBTVKpU1jAsMPsOqrftzfKaWV0XKuLkAcCQffdi/uGgdV6JjAJj+bC85iheimJMkLwQw4FE/jq9+hw5N7l6Z3tanDmXcXNBqVQKDz/DCB+vw6j+ZgbNWsfmPo6Skpec6TwcHDUf+i6T2s+/QYewCXlmygeWb97Dv+FluxubeqU12cUkpVCqre9b8tZuxuLuUMoybsuoHwq9F5/iMn3dtAKJi4q36cfK/H3bz5c6/ANAoCsN7PpSvGIUQ9kfOyQuhV7tKRfb/bzKz127j/a938nyP9ozq8zA7Dp3km91B/PL3CVLTM/jxj6P8+MdRyrqVZsAjrXm2a1sCWjbCwSHnb+Y+revT1Lcho5Z8zd8h4SbjvMqXoVm96jStW41mdavzWLumVK1Yzmxs7496ko+37DW8T0hJNbxOTElj5MK17F36huHpdQB92jdj73HdLXRBoRfxrVLG4rp/ufNPJq743vC+QXVPHBwc8igxIYS9kyN5IYw4Ojjw7otPErj4ddLSM3FxdqL/I635Yc5oIjcvZs3U4XRt7YOiKMQmJrNm5590m7yUmkOmMWnFRo6cvZijeb5/p5b8/O4YXJxNz+1HxcQRGHyGj37YTejlSMORutm4HB2ZPbyfxfF/nAhj2eY9JsOMe77bceikxc/+sD+YUYvXmwzr2MzbwtRCiOJEkrwQZnRp7cPrg7qZDCvn7srIxzoSuGQSVzctZOmYwfj71AHg+q1Ylv4QiP/o9/EZPpM567Zx3qgJvXf7ZuxaOB4PV5ccy2pcuypDu7fHyTH3hrWpz/SiQhk3i+Onf7aZs5cjDe+b1KmGk6PuaHzfcfOd4uwKOsWz735u6FEvS/N61XONRQhRPEiSF8KC3C46q1qxHBMHdiNo5ZucXT+P2SP64V2jMgDnIqKYvXYbrUcv4NXVu1jx8x9cv3WHR1s2Ys+Hk3Ik6tOXrtNi1FwGzlrFif+u5BrTsnFDLI5LTc/g+flryMjMBHTd5DasobsaPzQiKkcLw83YeNbu+otebZuQfVWzHnIjhCjeJMkLcY8a1vRi1vB+nF0/j39WvcnrA7tRtaLuCvjQa7eZ8cXP1Bg8je6Tl3Iy/Crb3x9rGN/TvwkN9bfF/fjH0TyT/XPd2lPLzH3xWf4Jvcji738zvO/cUtePfUpaOlejTbvCrVTWg+9mvkyXVj5k5f/S+lMKzerWKEBJCCHsjVx4J0QhURSFNo3q0KZRHRaNHsiOv4+x8sff+fPcNeKSUggMPkNg8BlKOTkS0LIRmVotDzf35pf5Y/luzz/M27CdcxFRhgv7BjzSmpnD+tK8vmnC/XLacLq+sdRiHO+s+Zm+DzWnad3qDHi0NR9v2QfAvn9DzU6f1Ue9m4sz2+eP4+l5q6lc3qNwCiWfToZfYdInm6hYxg3Pch54lvWgUll3PMu56//rhlUs64ajXBgoRJ4kyQtRBBwcNAS0aIhHRjxNmjXnQMhFkyv0f/1H10HN+1/tIPxaNM92bcuJz2eyaX9wnsm+S2tfmtWrzsnwq2aXnZGpZciczzj++Tu0b1wfRQFVhcDgnEn+ox8CuZOQDMDUZ3ryaMtGfPvOSza7P75ZvRp0ataA2Wu35Tqdi7MTs4b35Y3B3fO8lkGIB5k01wtRxMxdod/NzxeNRiEpNc1whX7dZ9/k6LnLrJs+kvUzRubajP/t26MAeLJTS3xqVsmxzNOXrjN3/S+4ODtRtYLu1IC5HwXGR/FvD+0DQEDLRoVfCHm4k5jCzn9O886anzl48nyu0z7XrR2h6+Yy/dnHJMELkQfZQ4S4j7Ku0B/5WEeu37rD93uP8M3uIP4JvWi4Qn/pD4E0rOnFkM5tKOPqwurtB80e2Xdu2Yi3hvamZf0aNHthLqERkSbLev+rnTzVqRX+PnX4+c9/uXHHtAOe7EfxxvfYF6Xk1DSOhUVw+Ew4QaEXORTyHxejbuf5uS6tfAi7EsW3e4LYFXSK2l4VaVavOg838+axdk2pVsl8HwNCPMgkyQthI1lX6E8c2I1zEbrk9XXgYcKu3OBcRBTz1m8HoE2j2jzXrR1/n/6P8Gs3Dcn+yU4tcXZ0xNHRkZNrZtL0hTmcjYgyzF+rqjzx9ie89Vxvfv7zX8h2db25o/jCptVqCbtyg8NnLhj+/v0vgoxMbY5pHTQamtWrTjvfuoRcvGY4om9atxofvDKAXm2bcjnqFvWefYtbcYncikvkaNhl1v36t+HzFTxcqV2lIi3q12D044/SplGdIlkvIYoLSfJC2IGsK/RnDutL8LlLfBMYxHd7/+H6rViOnL3EkbOXUBTdve83YxOIioljy8HjbDl43HBkf2rNLJqMnMO5K3cT/ZXoGA6dCc+xvHW/HSqSo/joO/FGCT2cf0IvccdCl7q1vCrQzqcuLepVxUNNYXDvLlTxrMSlyJt0fWMpbi7OeNfwAlXlhQ/WcSchOdeuhDO1WqJjE0jPzKRHm8a0rC93CAghSV4IO5L9Cv19x8/yze4gfvgjmLjEFEIuXgPA0UGDi7MTCcmpJs343749iqfnrSbs6g3DPNf9+jelSzmRnHJ3OSt+/gNwvKejeONm98NnLhAUepEL12+andbD1QX/RnVo51uXOlUqotVquRR1m9CISL7fd5Sr0beZ9s0+UtIyTD53/HyE1fHUq+rJ+6OeZEgX/wKtjxAlkSR5IezETz/9xHvvvUfp0qXRaDR88skndPVrQlc/X1ZMfDZHH/oJybr+6zWKglZVDcn+qU4tSU5LNzxNDiA1W/KMT0oBF3erj+K1Wi3nrkRx+LQumefW7K4ANb0qUMHdFUWjkJyazp2EJP4K+Y89x8zfxmeJs6MDHq6lqVzeg1qVy9OwhhfbD50kXP9jQlGgY9MGLB//NC0b1MrXvIV4EEiSF8IOBAUFMWzYMI4cOUKjRo1Yv349PXv25MyZM3h4eBiu0O//SGtiE5LYfOAY3+wOYs+x0Bxd0v508DgArqWcSErVNW9rzTzuNrej+Pw0uzs5OuCgKGRotWRkalGBy1G3uWzFxXTOjg64ly6FRylHGtSsSuM61WhevwZtferQuHZVklLTcXVxNtwTr9Vq+eyXAzg7OTIkoA0fjR1MhTKW+/wX4kEnSV4IO7Bw4UJ69+5No0a629eGDh3K1KlTWbduHWPHjjWZtmwuV+gby0rwlmQdxWdvdj94MoyrN2Otjj09IxNLSzJ3JG6cxB0dHYmPjyc4OBg/Pz88PEw74UmOS6LxiFk80rwh/To0p1m96rz9fG/efK73fbsbQIjiTJK8nVEUxRGoEhGhOxeZkJBAdHQ0V69exd3dPo5YJCbr5Cem33//nfHjx3Plyt3ubBs3bsy2bdt48sknc/3swPY+DGzvw+F/T/NrcCg7j4RyJVsXtgCk3j0S16Qn8/3OfSxe95Ou6b6AnBwdcCvtQqWy7lSvVJZ6VSvhU7sqrerXxLtGZRxzuY89MlJ3y19e5dSnVT0+27aHb3fsQaPR0Na3DmkJcXTz86VeNc8Cx25Jca9L94u5mGrWrFkDiFRVNSP3T4v7Rcn+0AphW4qi1ACsv9pICCHsS01VVXN/0pK4b6S9SwghhCih5EjezmQ11585cyYiOjqawYMHA7Bu3Tpq1bL91cMSk3XyE1NMTAwdOnRg4cKFPP7444bhb731FqdOneLnn3+2apkRV64S/N9V9p+8wMGQiySkpJpOkJoEx/TzavUElHIFoEX9GjzWtjHVKt7/HuPi4uJYvGgRAOMnjKdSpZzN73uPnzNcTJjFp1YVAlp407llQ5rWqVp49/kX87p0v1iKydfXtybSXG9X5Jy8ndHvHFcA3N3dDecta9WqhY+Pjy1DAyQma+U3prJly6LRaEymS0lJwdfXN9fPpqVnEBh8hk37g9ly8LjRFfBO4OJkeDgN6HqEy8z6YClXcNGdR/336h3+/ekvi0+9K0pXrlzh7deGA/BMz4dzrGtGZibLd82ilEc5urT2od9Dzen7UHNq5vK43XtREurS/WApJmmmtz+S5IWwA126dOHIkSOG96qqcvToUd56660c01pO7DrtfOuiKAqHToeb9GQ7b/hjvPnX1xZjyOsRt7YQcSOGD14ZQHe/xriVLmXrcIQodiTJC2EHpk+fTrdu3Qj8M4iWTX3Zte1nHBwcGD5cd5SbV2Lv0KQ+gwL8aOVdi3HLvs3xxLn5Lz1FV+9KvJlLDKUcHUjNyLSrZF+3aiXqVq1ks+ULUdxJkhfCDvj7+zNs2nv0fOtT2maex1kDv2zfwYGQi3km9oGP+lHDszzfBB6mz/TlJKakmjTTv9i7E9Oe6WXSUmBOakYm5dxKU6mcO+evRttVshdCFIwkeSFs7FZsAi8v2cDmAyepWLYM78z4mE37g+n89po8Ezvo+pB/efEGVm8/AECFMm7EJiSTqWrp0sqHla8/i6IoJvOpVqks1xIyye5OYjJpGRl8+NpgVm3bb/YRt5LshSg+JMkLYUO//RPCiIVruX5L18PcrbhE+sxYbjKNucSe5ezlSAbN+dTQPN+hST1CLl4nU6vFt3ZVfpw7GiczHdKM79eB6d8eMBtTUmo6U1ZtInDJ61yJvsO8Ddsl2QtRTEmSF8IGklPTmP7ZZpZt3mN2fG6JPcs3gYd5eclXJKakotEoTHu6J9/tPUJsYjKe5TzYPn8c5dxdzX62XcOaVK9Ujqs37/aMZ9zXfaZWpfPrH/L55GGEfDmb7/b8I8leiGJIOsMR4j7793wE/qPft5jga3lV4Nt3RjFxYDezCT6ref65974gMSWVqhXLsnPBePb/G8aF6zdxcXZi63tj8rxg7b0XTbvLTU5Nx6u8ad/xoxavZ/qnPzK0e3tCvpzNhjdfoGFNL0B3NX6LUXMZOGsVJ/6TO6eEsEfSGY79UoFcH95hKxKTdbLHpNVq+XBTIG99sYW09Jx9hSiKgouzIy7OTjSpU42t742hvIebyTTZm+e7t/Fl/fSRTFyxke/36i6s2zjrZQYFtMkx/ytXrlCzZk0Azpw5Q6NGjaj4+OvEGJ33r1+tEmnpmUQYPaYWoJd/E7YvGIdGoyEjM9PkyD5LQY/s7W3b2Vs8UKxiUnL7jLj/pLleiPskNjGZzi0bEfzpW7g4O+n/HCnlpPvv6OCQ4wI5Y9mb5+eOfJwZzz7GzC+3GhL8/JeeMpvgzVEUhenP9mLaZ5sNw/67dpP/jRnChz/8ziWjR8Xu+icEn+EzOb76HVxdSjG0e3ue7uIvzfhC2DlprhfiPinv4YZfo9o0rVudBtUrU8OzPJXKeuDh6oKTo6NJgk9Nu/vwVnPN83uWTOKtoX1Y/9sh3vtqB3D3Vrn8mDS4O6VLOZkMe2PVJo5++hZ1qlQ0GR525QY1Bk3jctQtQHfvvrOjgzTjC2HHJMkLYWe2HDxmODI/ezmSdq/NN9we172NL8dXv8OjLRux91goLy1eD0DX1uZvlcuLo4MDrz0RYDIsI1PLE++sJGzDPOpWNU30MQlJeA99m4Mnw/jq98OMWLCWtPQMOWcvhJ2SJC+EHbkcdYsXPljH8fMRfBN4GL9X3uNk+FU0GoV3X3yCXQsnULl8GUIvX6f/zFVkZOpulfthjvlb5awxZ8TjODmYfhUcPHmeXf+c5tz6edSvavrQmLSMTB6ZsIh3v9pOclo6A2atAnQ/GCTZC2FfJMkLYSfSMzJ4Zt7nxMQn8dkvB0ya53cvfp0mdaqh0WiIvhNP7+nLuZOQlOetctZwK12KZ7u1zTH86bmrAQhdP4cG1UwTvarq+pUH2BUUwu9HThvGSbIXwn5IkhfCTsz6cht/hfwHQKL+MbFZzfPOTk68vOQrYhOSePLtT/J1q5w1PnhlIBp9U39Wg39iSirD5n+Jo6MjZ9bNwbtaZYufHzznU7RarckwSfZC2J4keSHswO9HTrPg2105hjtoNFyMvMXSH34n+k48bV+bb/ghsH7GSNo3rlcoy69cvgyPtWsK6O/d1Pt2zz8cOXsRR0dHfls8AY2FU/53EpIZuXCt2XF5JfvnF6zjv6gYs58VQtwbSfJC2Fjk7ViGvv8F5vqsOBsRxdeBh9l84BiA4b7090dZf6uctf43dojhdWnnu1fc93tzBQB1qnoS/8syyls4NbD+t0McP3/Z4vwtJfuf/zrBqFU7eX7BOjmyF6KQSZIXwoa0Wi3D5q/hRky8YVgZNxde6vMwB5ZN4b+v38NBo0GrNf0BsOj7X+k/cyUXrt8stFjqV69Mhya6loFko1v4Im/HMu3THwFwdXXhxk+LaVjDy+w8+kxfbna4sezJvkF13fn+n/86Ic34QhQySfLFgFarJSAggDp16uQYFxsby/PPP0/btm1p3bo1c+bMMXtEWBhSU1OZNWsWjz32GG+88QadOnXiqaeeIjw83GS6q1ev0rdvXzp06EDr1q1ZtWpVkcQDcPv2bWbPnk2PHj2YOHEiHTt25N133yUjw7RHufsZU5bz588zduxYevfubXZ8bGwsfk+9yO9HzoCq4l2hFN/NfInIHxfz2eTn6dTMm/ikFD7fcTDHZz3LeTBxQO+CvygAACAASURBVNd8nY/fuXOn4fXzzz9PSEhIjmk+Mjqar1KhjOH14u9/M9wf7+joSMiXs2hkJtFfuxXLlJWbzC4/LS2NGTNm4OjoyMWLFw3JPujjKbz51EN4ujsDd5vx+0xdWuTJfuPGjfTo0YOuXbvi7+/PgAEDuHDhgmG8qqrMnTuX1q1b07ZtW4YOHUpsbGyRxPLzzz/Tt29funfvTqdOnfDz82Pjxo0m09zPeMxZvnw5iqKwb98+k+GffvoprVu3RlGUPxVF2a4oSvX7FpTInaqq8meff6qqqmpcXJw6btw4tVy5cmrt2rXV7Pr166eOGDFCVVVVTUxMVJs0aaJ++OGHOaYrDNevX1erVq2qnj9/Xt27d696584dddCgQWqbNm0M02RmZqotW7ZUZ8+eraqqqt64cUP18vJSf/zxxyKJacOGDWrjxo3ViIgIde/everZs2dVLy8v9Z133rFZTKqqquvXr1f9/f3Vpk2bqp06dTI7TcfH+qsVe7yofrjxNzX8SqTZbffhxt9UAl4y/Dl2fUV9c/VmNTk1LV/xHD58WHV1dVXRnXJX58+fr1avXl2Ni4vLMa3v8JmG5bk/NtbwuvHwmSbTpaenq42Gvm0SHwEvqU5dX1H/u3LDZNoLFy6o7du3V4cNG6YC6oULFwzj4uLi1Dlz5qielb3UFT/8qjZ83nSeA2auVP89H2EyP61Wq16OupWvMjDHyclJ/fXXX1VV1dWT4cOHq/Xr11d//fVXNS4uTl2yZInapEkTNTExUVVVVR05cqT6+OOP3/NyzenZs6e6bt06w/utW7eqGo1GPXHihBoXF6fu3btXff/99+9bPNldvXpVrVWrlgqoe/fuNcT01VdfqV5eXmpUVJSq6g4wZgLHAI1q++/RB/7P5gHIn8U/VVVVNTQ0VK1fv746ceLEHEn+xIkTKqCePn3aMGzFihVq5cqV1czMTLWwpaamqkePHjXs3HFxceqyZcvUMmXKGKbZunWr6ujoqMbGxhqGTZkyRfXz8yv0eFRVVXfs2KF+8cUXJjGNGTNG9fb2tllMqqqq27dvV2/evKn27NnTbJI/ceKEipNLrtsuPSNDrT1kuiHZtXnlXfV42OUCxdO/f3+1b9++hiQfEhKienl5qcuXL88Z+98nDMts/sJsk4S74qc9JtNaSvQ93vjQ5IfIyZMn1bCwMHXv3r1mk7y3t7c6ceJEw3p/umW3StvBFpO9VqtVaw+ZroZdiSpQeWQZOHCgyft//vlHBdTly5erMTExqqenp/rJJ58YxoeEhKiAevLkyXtarjlHjhxR09PTDe/j4uJUQN28ebMaFxenBgYGqpUqVbpv8WTXv39/deXKlTmSfMuWLdWpU6dmTQZQFkgH+qq2/x594P+kud7OTZ06lZdeegkXF5cc4wIDA3F3d8fX19cwzN/fnxs3bnDixIlCj8XZ2ZlWrVoZ3l+7do1169YxYcIEk5gaNWpEmTJ3m3r9/f0JDg4mJqbwr6B+7LHHeOGFF0yGubi4kJaWZrOYAHr37o2zs7PF8YGBgbiXcsx12205eJxLUbcoXcqJJa8O4u8V02nRoGaB4tm9ezctWrQwvNdoNPj5+REYGJhj2sfaNaV6pXIAnAi/SrO61QzjXl+xkTijB9o4OjpyykzT/W/BZ+g59SPiEpMBaNq0KQ0aNDAbW0xMDGFhYbRu3Vo3TwcHXn6iC74Jp+hZy9nirXeXom7x8PgPOBle8Cb9TZtMTy1k7WcZGRmcOnWK6Oho/P39DeN9fX1xc3MzW273ys/PD0d9h0bp6eksWrSIxo0b0717dwDCw8O5efPmfYvH2LZt23BycqJXL9Nuk+Pj4zl+/LhJTKqqxgLngG5FGpSwiiR5O7Zt2zYcHR1p166d2fHh4eF4eZl+uVapUsUwrqhcu3aNl19+mRYtWtCzZ0/mzp1rElNWDNljMj7XWZT+/vtvBg0aZFcxZWfNtvtw0+908/Pl1JrZTBrcHUcHhwIt69atW8TGxlK5sul97lWqVDFbTxRFMXkMrfHjbtMyMnn87U9MpreU6P/4N4xHJiziRkxcrvFdvHgRIEd5VK1SBeeYy2ZvvWv50jwAIm/H8ejExQSdKZzt+Pfff1O1alWaNm1qiMu47iiKgpeX1//bu/PwmO72j+PvmWyyEoTU0kUb+xLSBKEVS7Ul6qELpTxt/TxVpWhLFVXaCkpVLaWptqittFoldm2KqiWxRqJJq5aQRQjZt5nz+2NkmEwSg5nMZNyv65rrSs45M+eenJl8Zs453/tY9P31xhtv4OPjw65du9i2bRseHh6A7n1njXqys7OZOHEin332mdG80mq6Lhkwz/hOcVck5G1UVlYWEyZMYMaMGWUuk5OTg4uLi8G04t9zcnJKu4tZ1KlTh/DwcI4fP8727dsZOnSo1Wsq9vvvv3Pu3DkmTZpkMzWV5lY1JSSm8L/Qx9k+azQNSnSbu5N1AUZ7FlxcXMp8/gOfaKvvorc9Ko6B3W580Pz9WDyb/jTcU1Qc9I3rG/6zP/ZPIu3emMGZ5LJHAeTm5pZbX1lD74qlZ+bQ9e05/HbkVJnrMEV+fj6zZs3ik08+wdHRUf+3KW07WfJ1s3DhQi5fvkzXrl3p0KEDSUlJ+vqsUc/777/PsGHDuO+++4zmlVUTkA/ceRtGYTYS8hVMpVJNUalUyi1ujxa/sUr5hKzn5uamf5MVK/7dzc3099eUKVNQqVTl3qKioozud9999zF9+nSWLFmiP1PbmjVdunSJ0aNHs2HDBqpWraqfbu2/U2luVZNfvdq8/FTwbV9wpqx1AQaHMIrXV9bzd3RwYMJA3a5ZjVaLq7MTVd1vHDIa8PESoxEMjo6OnPhmslHQ/5uURtvh04n590Kp63J1dTWpPkcHB/p1fpTQdi2NHiMrN5+n353Hxn3HSl2HKV577TWee+45evfuDdz4u5W2nW7ndXMnHBwcmDJlCoqiMGfOHOBGkFZkPUeOHOHAgQMMGzas1Pll1QS4ANb5BC0MSMhXvNnAfbe4Hf3111/5/vvv6dGjB6NHj2bVqlUkJycTEhLC//3f/wHQoEEDUlJSDB48OTlZP89U77zzDklJSeXe/P390Wg0aDQag/s2atQIgNjYWP16i2soWdNDDz1k9pqKXblyhYkTJzJnzhz9sd1i1qqpPObadqaoUaMGVatWJTU11Wh95a1reO/O+qY4y3fsZ+Kgnvp5mTl5DJ7+rdF9ygr61PRMOoyYyYlzl4zuUzw0tLS/x831KYrCzNXbWBtZ+gep/MIi+k5exOpdB8t8TmUZP348jo6OTJs2zaium187iqKQkpJi9m0Exh9y1Go1fn5++vdWnTp1KrQegE2bNpGbm0uXLl0ICQmhf//+AIwePZoePXpw/UQ7o/cX4AtY7hiCMJmEfAVTFCVLUZTkW9yKjh07xu7du9m8eTNz585lwIAB+Pr6EhkZyZIlSwDo2rUrWVlZnDp1YzdlVFQUtWrVomVL4287ZfHw8MDX17fcm6OjI999953RcbniXYnF/4C6du1KfHw8mZk3mrtERUUREBCAt7c3pjK1JtCd/NOvXz8GDx5M586dAQgPD9c/ljVquhVzbTtTdenSxeBkTEVROHz4MN26lX1ulLurCyP66P6eBYVFXMvModXD9fTzi1vellRW0Gfk5PHO8l1Q3fDkQW9vb/z8/Dhy5MiNZTMyiI+PN6hPpVIxaVBPzq+dyZVfPmPPvLF8MXoAw3uH8FhLP6p5uFGk0TJw2teEb9xt2h8GmDlzJmfOnCE8PByVSsWRI0f466+/aN68OT4+PgZ7Z06dOkV2dna5f7c7VfLDKejeX8XvrQYNGlCzZs0Kqwd0u+oPHz5MZGQkkZGRrFmzBoC5c+eyefNmGjduTKtWrQxqUqlUXkBDwLJnAwrTWPv0frmVeVMURdEPUxk/fnyZ4+RfffVVRVEUJScnR2nRooXy6aefGi1nDt9++63SpEkT5d9//1V+++03JTU1VQkNDVWaN2+u5OfnK4pyY0z6hx9+qCiKoly6dEnx9fW12Jj03NxcJSQkRBkxYoSyePFiJTIyUjl06JDSpk0b/TIVXVOxjIyMMofQKUrFbrsDBw4o7u7u+iF0M2fOLHOc/M1S0zMUh66vKYQMVdyfekPZfuikwbC2+559R1EURckvKDQa3ldYWKg0HvS+0fA6Og1R5qzcqF+ueJx87dq1ldRU3fj6jz76SPH397+toaBarVZJTL2ibD0Qo8z+fpsSfz75lvdZtGiR0qxZM2Xfvn3KoUOHlEOHDinjx49X3n33Xf04+ebNm+vHpQ8ZMkTp1auXyTXdDpVKpWzatEn/+3fffaeo1Wplz549BuPkK6qe0vz777+ljpP39fUt3nYAk5Bx8jZzs3oBcivzpiiKoiQkJCitWrVS7r//fsXFxUXp1KmT8u233xbPVtLT05WBAwcqgYGB+oYvWq1WsYRz584pI0aMUFq1aqW0bNlSadWqlfLSSy8p584Z/nM/f/680qNHD6V9+/ZK69atDcb1mtuCBQv0wVXyZq2aFEVRNmzYoHTs2FHx9vZWqlatqnTq1ElZsmSJwTIVue0URVHCw8P1f5tHH31UiYmJMel+/53+jT6gZ6/Zprw0bYlBaI9b/IMyY9UW5Y25K43uW2bQhwxVWvUcqCiKLuTXb9qifDpnjtK6dWulffv2So8ePZTz588bPZ45ZWRkKGq1utTXTnHIa7VaZerUqYq/v78SGBioDBgwQElPT7dIPfPmzVPat2+vdOzYUWnfvr0SHBysD/3iQL127VqF1VPSqFGjlLZt2yqA0qpVK6Vv3776sF+0aJHSunVrBdgHRAD1FOv/D5WboqBSFMu0QBV3TQHdrujo6GgCAgLw9PS0dk2A1GQqW6spMTGR+vV1u8rj4uJo3LixSfc7ffESDw+cCIC3hxuHwyfR/NUpZOfpjiGrVSqqODvhW8OLv1dMMzpZsKioiBavfsip80bHbXlvwNOM79eVdxespGnDRxj53BN38xTNwta2G1Sqmu7+TFFhVnJMXggL+/vvvwkODiYkJKTU+RV5/YE70aCODz3b6S5Dm56VQ8T+E4zs20U/X6so5OQXcPpiGn9fSDW6f1nH6AGmr9rCmwvX8Wf8BaYsj+BKRrblnogQ9yAJeSEsaPv27bz22muo1WW/1QYNGoSjoyMHDx5k7969rFu3jrlz51Zglbf24Su99T9PXb6RXYdLH5O+9aDxRW+g/KBftv0Ax86mciUzh0lf/2yegoUQgIS8EBbl5eXFli1bymzpeuLECTZu3Mi4ceMA3djs4cOHM2PGDLRabUWWWq42DR+gXVPdcMNLV7MY3juEji2Mn1PE/rLbKZcX9MUWb9zN4fizd1+wEAKQkBfCotq1a3frHvZmuv5AYmJiubfi4Y536uZv8x8t38Rvc96iYT3DVrm7Dp8iN7+g5F31ioO+vk/pQxcVRWHEvNU29QFHiMrMtEG9osIVj+nOzs5Go9GQnW07xyqlJtPcXFNhYSEajcZgrD7oxjn7+PgYTC/uVX7y5Ekefvhhk9dXfFKdKXJycoxquZW2DevxSJ2a/H0xjdNJafwYeYgvR7/IE+/Op0ijC+UijZavN/3Of7u3K/exjn05ntbDZnI29YrRvD9Pnib8l98Y2DXotuozF1t/LdmK0mqylZMCxQ0S8jYqOjoaAK1WS25uLrGxseUe161IUpNpbq7p8uXL+rORb3b+/Hm0Wq3B9OIr48XGxlK3bl2L1JaQkEBGRvkXjilN/3YN+Xi9rg/9e1+tp4qTA12a3c/242f0y0xZuomm1R1R36Il75LXuvPqFxGcv2z8YWPCkg3Uq6LBo0rZe0EsxdZfS7ZcU1knlwrrkZC3UQEBAYDu0/LJkydp2rQp7u7uVq5K516vKSwsrNwLBwFERkbStGlTfU01atQgOztbv12L1a9fn1OnThlMT0zUXTq1adOmRsuXJy4urtz5ycnJ+o6Afn5++Pn5mfzYxVr5+xP+63FSr2bxb+o1AAY92ZH41EzOJF8G4HJWLscvFTDk6eBbPt6xr1oTNGIWf180vIBNenYeEbEpfDL0P2Xc03Lu9de3qWyxJmFMQt5G3bzby8HBAXd3d5vaFXYv1zRx4kRGjRpV7jI1a9YkNzdXX5OTkxMODg5GtTVu3JhVq1YZTM/KygKgWbNmt/VcbjXuvfgwAOhO8Ludx1YUhXFf/sihU2eMLnmbci2b+W++SK8JC/TT3l+6kec7B1G3jGPvNzu4YCythn5s9I3+m637GPZMCK0eMf0whLncy6/v22GLNQlDtrHfR4hKpDL3sL9TKpWK9wY8TUp6BhcvXzOYd+jUGULbt6Rnuxb6aVm5BYycv8akx3Z0dOSb4T1pWNfwJL6CQg1Tl22yqZ4BQlQ2EvJCWFHLli3p1asXs2bNAnTXVl+0aBHvvvuuzRx7LVbdy50tM9/Et7qXwfRj/5wHYO6Ifjg73fhw89OeI/y05wimcFSr2T//baPhdT/tPcKwOSvkbHsh7pBt/RcRws788ccf9OjRg61bt3L06FFCQkL4+uuvDZZZvnw5+fn5BAUFERwczLPPPsuYMWOsVHH5HvStScT0kXi4uuinZecVcDjhLI/UrcXYft0BKD7n7o3PV3Ety7TLipc1jj580x7+O+Nbikpc5lgIcWsS8kJYUIcOHdi8eTPJyclcvXqVyMhIhgwZYrBMtWrVWLFiBQcPHuTIkSN88MEHRv3fbUmbhg/ww5RhBmfPf/DtRkDXi75+LW8URdfTPunyNcZ/9ZPJj11W0K/YcYB+U8PJLyg0z5MQ4h4hIS+EuG1PBjVjydjB+t837z9BQmIK7q4uzBn+AqDraQ+w+Jff2XsiweTHLivo1+85wn/e/6LcZjtCCEMS8kKIO/LK0x14f1AooAv0mau3AfDs423o2kZ3pr+zo+5M/P99uuK2voWXFfRbD56kx/h5ZObkmeMpCGH3JOSFEHds6iu9aN+0AQDLt//J+dQrqFQq5o3sj6ODmoIiDSoVxJ1NYsbqrbf12GUFfeTReLqPnUt6pu10fxPCVknICyHumEqlYtusUXi6VaGwSMPs77cD0PTBOox6tisAapXu30zYyi3Enb29/vllBf3+2NN0eWsOl67eXmteIe41EvJCiLvi6ebKewOeBuCriD2kpuva5U4eHIpvdS80Wi2uLk4UFBYxdPby2x4OV1bQH/37PJ1Gz+bCpXTzPBEh7JCEvBDirg3v3Ymq7q7k5hfy+Y+7APByd2XWsOcAyM3XHY//I+Yfwjftue3HLyvo484m8fjoWZxJTivjnkLc2yTkhRB3raqHGyP7dgFgwc+/cfX62PiB3drqrzvveX1s/bvhP97Rt+/Sgl6lgtMX03jszVnEn0+526chhN2RkBdCmMWoZ7vgVsWZjOw8vvg5EtAds5//5ouo1Soyc/NxdXEiIzvP5Ja3JZUMekXRrSPxUjqPj5rFidOJ5no6QtgFCXkhhFnUrOrJa6GPA/DZDzvJzs0HwP+R+rz+TCcAtFrd2PnbaXlbknHQK6hVKlLSMwgZ8ylRf525y2cihP2QkBdCmM3bLzyBs5MjadeyWBKxVz/9w1d6U7OqB/mFRdT21vW+v52WtyWVDHqtouCgVnMlI5sub825reY7QtgzCXkhhNnU9fHm5SfbAzDr+236BjjVvdyZPrQPACnpGTg7Odx2y9uSSga9RqvF0UFNZk4e3cfOZUdU7F0+GyEqPwl5IYRZjev/JGq1igtpV/lux3799Fef7kBg4wcBqO7hDuha3v4Ze/qO11Uy6Is0WpwcHMjNLyR0wgI27jt2509ECDsgIS+EMKuH69aif+dAAGas2qq/epxarWbBmy8CkJyeQd2a1QB4c+EPFBTd+RXmSgZ9oUaDs6MDBYVF9J28iO9/PXQ3T0eISk1CXghhdu8N1DXH+efiJdZFRuunBzV5iCE9OgJwNSsXlQr+Op/C6r13t2u9ZNAXFGlwcXKkSKNlwLQlfLvlj7t6fCEqKwl5IYTZNX+oLr07tAIgbOVmgy5304f2oZqHG9l5+TS5/z4AVu49yV93Oc69ZNDnFxZRxdkJrVbh1U+WsfCn3+7q8YWojCTkhRAWMWFgDwBi/r3Ipj+P66f7VPPko1efASD2bBK1vT0p1GgZuWDtbbe8Lalk0OcVFOLq4gTAiHmrmXmbF8kRorKTkBdCWERQk4foFtAEgGkrNqNcv748wLBnOtGyQT0A3KvoOuHtjztzRy1vSyoZ9Ln5hbhXcQZgfPh63v9mg0EtQtgzCXkhhMVMfEn3bf7gqTP8eviUfrqjgwMLRulOwjudlEajOtWBO295W1LJoM/OK8Djelvdj7+L4O0v1knQi3uChLwQwmI6tWpI+2a6682HrdxiMO+xln4M7NYWgAtXsqjq4XpXLW9LKhn0Wbn5eLlVAXQd+YbNWXHXhweEsHUS8kIIi1GpVPpj878eOcX+EmPiP3ntWTxcXcjKK6DlQ3WBu2t5W1LJoM/IyaOquysA4Zv20HfyIgqLisyyLiFskYS8EMKierZroT/+HrZys8G8OjWrMb7/EwDsjfmHoCYPAnfX8rakkkF/LTsXb083ADb8cYzHR83Wd+YTwt5IyAshLEr3bV43bn7jvuMc/8fwSnHDQh/j/ppeKIpCYZGGKs6Od93ytqSSQZ+emUN1L13Xvf2xp+k9aSG5+QVmW58QtkJCXghhcc91CsCvXi0Apq8yPDbv7OTIyKcCADiScJ5ngnXj6xf/8rtZLzRTMuivZGTr5207FEuP8fPIzMkz2/qEsAUS8kIIi3NwUDP+xacAWBsZRUKiYeObRx++j97BLQGIPBpPi+vH5//36Qqz7krXKjDztb64ODkazYs8Gk/3sXNJv36YIObfi1y+lmW2dQthDRLyQogK8dIT7ahfyxutVmHm6m1G86e92gtXFydSr2bS/KE6qNUq4s4mMcNMDWwUReHTtTt4YWo4+YXGJ9up0O267zVxEVez81i3+zBTl20yy7qFsBYJeSEsKCMjg7CwMDp27EhISAj+/v58/PHHFJU4o/vChQuEhoYSHBxMmzZtWLx4sZUqthxnJ0fG9nsSgOXb/+R86hWD+ffXqq4/E39tZDQDu+qG14Wt3ELc2aS7Xr9KpeK9gU+TsOJjXnkqGLVaZTBf7aDGQa3m+L8XGb10Jz/9cZwvNkSaZd1CWIuEvBAWdODAAX7++WciIiKIjIxk8+bNLFiwgA8//FC/jFarJTQ0lMDAQPbt28e2bduYMmUK69evt2LlljGkRwd8qnlSWKTh07U7jOa/0687DerURKPVciYljftrVaegsIihs5ebbUx7/VrV+ebdlzm2ZDKh7Vvqp2s0Wur5eOPk6MDZtAzOJF9Go9XyzqJ1ZlmvENYgIS+EBXl5eTFy5EiqVq0KQJ06dXjuuedYs+ZGw5eIiAhiYmIYM2YMAD4+PgwePJiwsDCr1GxJblVceOv5bgCEb9pNanqGwfwqzk58PqI/AHuO/82AbkEA/BHzj1la3t6s+UN12Rg2gsjP3qZWNU8AzqZcxtXZyWC5zQdi2HbwpFnXLURFkZAXwoLatm3LoEGDDKZVqVKFgoIbw7V27txJo0aN8PLy0k8LDAwkOjqa9HTTW7wmJiaWe0tKso3dzq8/04mq7q7k5hfy+Y+7jOaHtm9Jz3YtAPhu+36e76Q7895cLW9L6uTfiIs/fELrR+4HdA1zSnrri7UUae78mvdCWIvxKabCJmRmZgKQnZ2NRqMhOzv7FveoOFKTacqqae/evfTu3Vu/jePj4/Hx8dH/DugDPyYmBn9/f5PWV79+fZNry8nJMVhfRVID/+vZgVlrd7Lgp98Y3Nmf7Lx8th88QfcgXbh//HIoO6JiuZB2lRqernh7upGemcPrc1awcsLLFqnrt9kjGTF/HSt2HTSaF3s2iXk/7GBojw4WWfetVJbXt6enpxUrEqWRkLdR0dHRgO54bW5uLrGxsajVtrHjRWoyTWk1HT58mNOnTzNp0iT9Nk5JScHZ2Vn/O8Dp07r2r0ePHkVjgW+QCQkJZGRk3HpBC+nwgBfznRzIyMnjkxWbOJ2SjreHKzUcbuzheKF9Y1bsOcmSzft4pXMLvtp1jI37TzB3xc881sT0DzS345UOD5N+JY2II7q/v5uzIzkFupMkpy6LwM9Ljaers0XWXZ7K8voOCQmxblHCiIS8jQoI0O2izM7O5uTJkzRt2hR3d3crV6UjNUFYWBgzZswod5ktW7bg6uqqr+nixYt88cUX/PjjjwbfzmvXrk1eXp5+mwPk5+cD4O/vb/I3+bi4uHLnJycn07lzZwD8/Pzw8/Mz6XEtZUh8Ggs37Oa7PbEUajQ83uJhg79B42bNiYz7hMS0q5y+kkdIy0eIPP43X+w8xit9ntT3oDe38EaNGDp7OZuPnCanoIiOzR/mbMoVzl9KZ/tflwgb8oxF1lseec+JOyUhb6Nu3u3l4OCAu7u7Te0Ku9drmjhxIqNGjSp3GRcXF44dO4a7uzuFhYUMGDCAxYsX89hjjxks17BhQ3bt2mVQd/G37ObNm5v8fBo3blzufA8PD/3Pbm5uVtt2P+89wntf/URuvq7JTeH1PRWnky4b1OTp6clnI/rx/JQv2XXkLxaNGciBv86SfCWDsNU7+GLMQIvV+HavttTyqcXS7fvZG/MP/9ezI2387mf22u28+Vw3/OrVtti6y3Kvv+fEnbGN/T5CVDIeHh74+vqWe3N01H2GzszMpFevXkyePJlu3a6fWR4ern+srl27Eh8fb3CMPCoqioCAALy9vSv2iVWA/3RszX86+nM25bLB9MS0q2TlGp709uzjbejaRvfhZebqrUy8Po5+0S+/88eJvy1Wo1qlYu7wZxnaU/eBbEnEXo79k0jM1x9QWCQn4InKQ0Jea4N12wAADzRJREFUCAsqKCigf//+tGvXjrp16xIVFUVUVBRffvmlfpnQ0FCaNWvG3LlzAUhLS2P58uVMmDDBWmVbXNj/9eHVp41PYos/b9juVqVSMW9kfxwd1JxJvkx+URGtHtZd0W7op99Z9OpxarWaxW8N1Af9lxt3M+aLdTS+39di6xTC3CTkhbCgiIgI9uzZw5w5cwgMDNTfDh8+rF9GrVazceNG9u/fT3BwMN27d2fy5Mn07dvXipVblkql4su3X6JXcEuD6afOJRst2/TBOox6tisAs9ZsZ+orz5i95W1ZSgv64XNXma0xjxCWJiEvhAX16dOHjIwMFEUxut2sXr16REREsG/fPg4fPszrr79upYorjqODA2veH0q769eQB/irxDf5YpMHh+Jb3Yu8gkKWbt3HqL660DdXy9vySNCLykxCXghhNW5VXPj+/SE86KPrCFjaN3kAL3dXZg17DoCf9x7lsZaP8EDtGmZveVsWU4Jeo5HQF7ZHQl4IYVXeHm588lJn6vt4lxnyAAO7taVji0cAeDd8PfPe7AdYpuVtacoL+tT0DKav2mLxGoS4XRLyQgir8/Fy46epQ7mSmV3mN2KVSsX8N19ErVaRkJhK3NlkBnTV9ba3VMvbksoK+h93H2bm6q2kXLFegyEhSiMhL4SwCQ3r1eaHKa+Rdi2rzGX8H6nP6890AuCj5RGM7ded6l7uZGTnMXL+mjLvZ06lBf3bi9aRlZvPxysiKqQGIUwlIS+EsBltmzagdnWvcpf58JXe1KzqQXZePjPXbGPO688D8NOeI/y050hFlKkP+uI9CcWNfRb/8jv/XEitkBqEMIWEvBCiUqnu5c70oX0AWPPrIe6vXZ1uAU0AeOPzVVzLyrF4DUcSztF97FzW/HbIYHqRRsukbzZYfP1CmEpCXghR6bz6dAcCGz8IwJvz1zB/ZH9cXZxIunyN9776yeLr93+kPuP6P0nLBvWM5q359RDRf521eA1CmEJCXghR6ajVaha8+SIAMf9eZNuhWKb8txdg+Za3oDsJsHtgM6K/nMjKiUN46L6aBvPHf7XeousXwlQS8kKISimoyUMM6dERgMlLNzCgW1CFtbwtplarGdCtLaeWfci8kf2pWVV3EaCd0XHsiIq1+PqFuBUJeSFEpTV9aB+qebiRkZ3H+9/8wpKxgyus5e3NnJ0cGdm3C/+snMbkwaG4V3FhfPh66YonrE5CXghRaflU8+SjV3XXd1+6dR+FRZoKbXlbkpe7K1NfeYa/V35Mu6YNKuxsfyHKIiEvhKjUhj3TSX8C3IjPV/PBf0MrtOVtaXyrV2Xh6AE8GdSswtctxM0k5IUQlZqjgwMLRulOwjuccI41vx5i8VsDgYpreVsWD9cqVlu3ECAhL4SwA4+19GNgt7YATPj6ZwIbPVjhLW+FsEUS8kIIu/DJa8/i4erClYxsJn2zgc/eeKHCW94KYWsk5IUQdqFOzWp8cH2s/Jcbd5N4Kd0qLW+FsCUS8kIIu/Fm3y40vt8XRVEYMW81Lz3RVt/ydsS81RXS8lYIWyIhL4SwG85Ojswb2R+AP0+eZsWOAyweM5Aqzk5cTLtaIS1vhbAlEvJCCLvyxKNNefbxNgCMC/+RmlU9mPJyxbW8FcKWSMgLIezOp68/j6uLE6npmUxZtpG3nu9W4S1vhbAFEvJCCLvzgG8NJgzsAcD89b/x1/kUq7W8FcKaJOSFEHbpnX7daVCnJhqtlpHzVhPQ8AGrtrwVwhok5IUQdqmKsxOfj9CdhBd5NJ61v0Xx4avPWL3lrRAVSUJeCGG3Qtu3pGe7FgC8vWgdgM20vBWiIkjICyHs2twR/XB2cuRC2lWmrdjMU0HNpeWtuGdIyAthQQUFBUybNo1OnTrRrVs3WrduTZ8+fTh9+rTBchcuXCA0NJTg4GDatGnD4sWLrVSx/Xmkbi3G9usOwKdrdxB/PoXP3nhBfx16aXkr7JmEvBAWlJWVxbJly1i7di07d+4kOjoaJycn+vXrp19Gq9USGhpKYGAg+/btY9u2bUyZMoX169dbsXL78t6Ap6lfy5vCIg1vzl9DdS93ani5A9LyVtg3CXkhLMjT05N169ZRu3ZtANRqNY899hjx8fH6ZSIiIoiJiWHMmDEA+Pj4MHjwYMLCwqxSsz1yd3VhzvAXANh26CT/mfQF/1y8ROtH6gPS8lbYLwl5ISzIycmJVq1a6X+/cOECy5YtY9SoUfppO3fupFGjRnh5eemnBQYGEh0dTXq66ceLExMTy70lJd27Q8aKNBo6tWpIaz9dqEfsPwFAUJOHpOWtsGuO1i5AlC4zMxOA7OxsNBoN2dnZVq7oBqnJNDfXdPHiRfr3709cXBwjR45k7Nix+m0cHx+Pj4+P/ndAH/gxMTH4+/ubtL769eubXFtOTo7B+qzJ0ttOURQ+WBbB3PW/Gc07HH+W917szgfLIlj0y+/0CW5BiwdqcSrxEo0b2+ZryVaUVpOnp6cVKxKlkZC3UdHR0YDueG1ubi6xsbGo1bax40VqMk3Jmj777DPS0tKYNGkScXFxvPPOOwCkpKTg7Oys3+aA/sS8o0ePotFozF5bQkICGRkZZn/cO1ER2653i/vIzfDny51HDaZHx5/j/d6P8nDtavyTcpWhs5cz75VuTP3hDzyqOFOvZlWL1HO7KsPrGyAkJMS6RQkjEvI2KiAgANB9Wj558iRNmzbF3d3dylXpSE0QFhbGjBkzyl1my5YtuLq6GtXk7OxM7969mTx5Mk2aNKF27drk5eXptzlAfn4+AP7+/iZ/k4+Liyt3fnJyMp07dwbAz88PPz8/kx7X0ipq2wUEBNCySUNGLlyHVqsAoFUUNO41+Hrcy3QZ+zln0zJ4e+Vukq/lcD4Het+0TaxJ3nPiTknI26ibd3s5ODjg7u5uU7vC7vWaJk6caHBcvTQuLi4cPnyYKlWqGNTUunVrAM6ePUtQUBANGzZk165dBssUf8tu3ry5yc+ncePG5c738PDQ/+zm5nZPbrvhfbtRp1YN+n/4FfmFRQDsiTnNkB4d6damCdujYvn7YhoAu2P+5b3B997f6HbYYk3CkG3s9xGikvHw8MDX17fcm6OjIzt27GDhwoUG9y0+Aa5OnToAdO3alfj4eINj5FFRUQQEBODt7V1xT+oe8Z+Ordn6ySg83aoA8Mu+Y/gP/YjtUbEGy+0+/jd5crU6UclJyAthYd999x1pabpvh3l5eXz00Uc0b96cwMBAAEJDQ2nWrBlz584FIC0tjeXLlzNhwgSr1WzvQvwbEfnZ2/hU8+RM8mU2fDycah5uBsvk5Bew90SClSoUwjwk5IWwoDZt2tCpUye6d+/O448/TnBwMNWqVWPz5s04OzsDurHzGzduZP/+/QQHB9O9e3cmT55M3759rVy9fWvT8AH+mD+OujW9cVCr+XPhuzx0X02DZbYePGml6oQwDzkmL4QF1apVi9mzZ9/ymGW9evWIiIiooKpEMb96tflj/jh2H0+ge2Az9i8cT8/x84iKPwfAlgMxzH79eStXKcSdk2/yQoh7Wl0fb/p30R06qeXtRcS04TzeRNdzIPZsEudSLluzPCHuioS8EOKep1Kp9D+7ujjxwfMdGdUnBIBth2LLuJcQtk9CXgghSlCrVHz0Si8WjRnIjigJeVF5yTF5IYQow7BnOtGyQT0URTH4ti9EZSEhL4QQ5Qhu/rC1SxDijsnueiGEEMJOScgLIYQQdkpCXgghhLBTEvJCCCGEnZKQF0IIIeyUhLwQQghhpyTkhRBCCDslIS+EEELYKQl5IYQQwk5JyAshhBB2SkJeCCGEsFMS8kIIIYSdkpAXQggh7JSEvBBCCGGnJOSFEEIIOyUhL4QQQtgpCXkhhBDCTknICyGEEHZKQl4IIYSwUxLyQlQArVZLUFAQDz74oNG8a9euMWjQIIKCgmjTpg1Tp05FUZSKL1IIYXccrV2AEPeChQsXkpCQQNWqVY3mDRo0iBo1anDw4EFycnIICgrCy8uLMWPGWKFSIYQ9kW/yQljYxYsX+frrr/nf//5nNO/EiRNs3LiRcePGAeDm5sbw4cOZMWMGWq22oksVQtgZCXkhLGzcuHFMnz4dV1dXo3k7d+7Ew8ODJk2a6KcFBgaSmprK8ePHK7JMIYQdkt31QljQvn37cHR05Omnn+bAgQNG80+fPk3t2rUNpvn6+urn+fv7m7yuxMTEcucnJSWZ/FhCCPsgIW+jMjMzAcjOzkaj0ZCdnW3lim6QmkyTmprKV199xc8//0xmZib5+fkoiqLftqA76c7JyclgWmFhIQCXL182mH4r9evXN3nZnJyc23psS7K1bWdr9UDlqcnT09OKFYnSSMjbqOjoaEB3VnZubi6xsbGo1bZxdOVer2np0qUsW7as3GUWL17Mjh07eOqpp7h8+TLp6ekkJSWRn5+v37YAWVlZZGRkGExLTU0FdN+8b55uTgkJCWRkZFjksW+Xrb2ebK0eqDw1hYSEWLcoYUQlQ3VsU2ZmpgK6T8snT56kWbNmuLu7W7ssQGrKysq65TeqGjVq0LFjRxwcHPDw8MDBwYFz586RkpJCYGAgDRo0YMGCBSxYsICwsDAuXryov290dDSdO3dm7969tGzZ0uS6Lly4UO785ORkOnfurF+Hn5+fyY9tSbb2erK1eqDy1OTp6amyclmiBPkmb6Nu3u3l4OCAu7u7Te0Ku5drMvXx9+/fT3R0NAEBAXh6ejJlyhSWLl3Knj179Mv07NmTCRMmcOHCBRo3bgxAXFwctWrVon379rf1ra34/mXx8PDQ/+zm5nZPbjtT2Vo9IDWJOyPf5IWoICqVagrwsqIoD5aY/gtwSVGUISqVyhU4ACxVFGWOmddfDzh//df6iqKUf6aeEKLSk5AXwsJUKpUvsAZ4EPAF9qML8aXX51cDFgANASfgZ+BDxcxvTpVK5Xh9/QDJiqIUmfPxhRC2R0JeCCGEsFO2cZqmEEIIIcxOQl4IIYSwUxLyQgghhJ2SkBdCCCHslIS8EEIIYack5IUQQgg7JSEvhBBC2CkJeSGEEMJOScgLIYQQdkpCXgghhLBTEvJCCCGEnZKQF0IIIeyUhLwQQghhpyTkhRBCCDslIS+EEELYKQl5IYQQwk5JyAshhBB2SkJeCCGEsFMS8kIIIYSdkpAXQggh7JSEvBBCCGGnJOSFEEIIO/X/e0YffVoCV3IAAAAASUVORK5CYII=\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "vectors = []\n", "for _ in range(30):\n", " m = randint(-10,10)\n", " n = randint(-10,10)\n", " vectors.append(m*a + n*b)\n", " \n", "plot_vector(vectors)\n", "pyplot.title(\"Thirty random vectors, created as linear combinations of $\\mathbf{a}$ and $\\mathbf{b}$.\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In fact, we can *still* fill up the whole plane with infinite linear combinations of $\\mathbf{a}$ and $\\mathbf{b}$—they span the full 2D space. We're not forced to use the unit vectors $\\mathbf{i}$ and $\\mathbf{j}$ as our basis vectors: other pairs of vectors could form a basis. With $\\mathbf{i}$ and $\\mathbf{j}$, we saw that the components of a vector $\\mathbf{v}$ are the scalars needed in its corresponding linear combination of the basis vectors. If we were to use another pair of vectors as basis, we would need a different pair of scalars in the linear combination to get the same vector: we are _changing the coordinate system_." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's see another situation... we'll make linear combinations of the vector $\\mathbf{a}$, and a new vector, $\\mathbf{d} = \\left[ \\begin{array}{c} -1 \\\\ 0.5 \\end{array} \\right]$," ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "d = numpy.array((-1,0.5))\n", "vectors = []\n", "for _ in range(30):\n", " m = randint(-10,10)\n", " n = randint(-10,10)\n", " vectors.append(m*a + n*d)\n", " \n", "plot_vector(vectors)\n", "pyplot.title(\"Thirty linear combinations of the vectors $\\mathbf{a}$ and $\\mathbf{d}$.\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*What's going on?*\n", "\n", "Well, the new vector $\\mathbf{d}$ happens to be a scaled version of the original vector $\\mathbf{a}$—we say that they are _colinear_. Thus, all linear combinations of $\\mathbf{a}$ and $\\mathbf{d}$ end up on one line, which is their span. Their combinations are not able to travel all over the plane!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Definition:\n", "\n", "> A **basis** for a vector space is a set of _linearly independent_ vectors that _span_ that space.\n", "\n", "We saw above that $\\mathbf{d}$ is a scalar multiplied by $\\mathbf{a}$: it is linearly _dependent_ with $\\mathbf{a}$. The vector $\\mathbf{b}$, however, is linearly independent with $\\mathbf{a}$. Bring in vector $\\mathbf{c}$ now: it can be written as a linear combination of $\\mathbf{a}$ and $\\mathbf{b}$: $\\alpha\\, \\mathbf{a} + \\beta\\, \\mathbf{b} = \\mathbf{c}$, for some scalars $\\alpha$ and $\\beta$. In 2D space, any third vector will be linearly dependent with $\\mathbf{a}$ and $\\mathbf{b}$: these two form a _full set_ of independent vectors (and a basis).\n", "\n", "In 3D space, two vectors that are linearly independent span a plane. We need a third vector that is not a linear combination of the first two to span the whole space, and form a basis. Any fourth vector will be linearly dependent as it can be written as a linear combination of the basis vectors.\n", "\n", "##### Key idea:\n", "\n", "> In a set of linearly independent vectors, no one vector can be written as a linear combination of the others. The only way to get the zero vector from a linear combination of all the vectors is to multiply them all by zero.\n", "\n", "**Note**: Plotting 30 vectors can result in a messy figure. When we want to visualize many vectors like this, we can simplify the plot by only showing the tip (head) of the vector, as a point on the plane. We'll do that from now on." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Matrices\n", "\n", "### What's a matrix?\n", "\n", "In many books, they'll tell you that a matrix is a \"table\" of numbers, ordered in rows and columns. Maybe that's enough for some people, but you will get a kick out of _seeing_ what a matrix does!\n", "\n", "Let's remember our friendly vectors from above:\n", "\n", "$$\n", " \\mathbf{a} = \\left[ \\begin{array}{c} -2 \\\\ 1 \\end{array} \\right], \\quad \n", " \\mathbf{b} = \\left[ \\begin{array}{c} 1 \\\\ -3 \\end{array} \\right] \n", "$$\n", "\n", "Our little experiment with 30 random linear combinations of $\\mathbf{a}$ and $\\mathbf{b}$ helped us visualize that they can span the 2D space, and nothing is stopping us from using them as a basis if we so desire.\n", "\n", "Remember also our vector $\\mathbf{c} = \\left[ \\begin{array}{c} 2 \\\\ 1 \\end{array} \\right]$. Choosing $\\mathbf{i}$ and $\\mathbf{j}$ as a basis, then $\\mathbf{c} = 2\\,\\mathbf{i} + 1\\,\\mathbf{j}$.\n", "\n", "Now imagine that we use the components of $\\mathbf{c}$ to make a linear combination of $\\mathbf{a}$ and $\\mathbf{b}$:\n", "\n", "$$\n", " 2\\,\\mathbf{a} + 1\\,\\mathbf{b} =\n", " 2\\cdot\\left[ \\begin{array}{c} -2 \\\\ 1 \\end{array} \\right] +\n", " 1\\cdot\\left[ \\begin{array}{c} 1 \\\\ -3 \\end{array} \\right] = \n", " \\left[ \\begin{array}{c} -3 \\\\ -1 \\end{array} \\right]\n", "$$\n", "\n", "This is a new vector, let's call it $\\mathbf{c}^\\prime$: \n", "\n", "- it has components $\\left[ \\begin{array}{c} 2 \\\\ 1 \\end{array} \\right]$ in the $\\mathbf{a}$, $\\mathbf{b}$ system of coordinates, and \n", "- it has components\n", "$\\left[ \\begin{array}{c} -3 \\\\ -1 \\end{array} \\right]$ in the $\\mathbf{i}$, $\\mathbf{j}$ system of coordinates.\n", "\n", "This will blow your mind. Arrange the vectors $\\mathbf{a}$ and $\\mathbf{b}$ as the columns of a matrix, and you'll see that:\n", "\n", "$$\n", " \\begin{bmatrix} -2 & 1 \\\\ \n", " 1 & -3 \\end{bmatrix} \n", " \\left[ \\begin{array}{c} 2 \\\\ 1 \\end{array} \\right] =\n", " \\left[ \\begin{array}{c} -3 \\\\ -1 \\end{array} \\right]\n", "$$\n", "\n", "The matrix $\\,A=\\begin{bmatrix} -2 & 1 \\\\ \n", " 1 & -3 \\end{bmatrix} $ when multiplied by the vector $\\mathbf{c}$ gives the vector $\\mathbf{c}^\\prime$.\n", "\n", "##### Key idea:\n", "\n", "> The matrix $A$ represents the **linear transformation** that takes vector $\\mathbf{c}$ and transforms it into $\\mathbf{c}^\\prime$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Matrices with NumPy\n", "\n", "Let's play around with this a bit more.\n", "\n", "We can define a NumPy array to represent the matrix $A$, as follows:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[-2 1]\n", " [ 1 -3]]\n" ] } ], "source": [ "A = [[-2,1], [1,-3]]\n", "A = numpy.array(A)\n", "print(A)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can use the NumPy [`dot()`](https://docs.scipy.org/doc/numpy-1.15.0/reference/generated/numpy.dot.html) method to multiply the matrix $A$ and the vector $\\mathbf{c}$:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([-3, -1])" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A.dot(c)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Sure enough, this gives the vector $\\mathbf{c}^\\prime$. Now let's see what happens when we multiply the matrix $A$ with the basis vectors $\\mathbf{i}$ and $\\mathbf{j}$:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([-2, 1])" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A.dot(i)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([ 1, -3])" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A.dot(j)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Woot! The matrix $A$ when multiplied by the vector $\\mathbf{i}$ gives the vector $\\mathbf{a}$ and when multiplied by the vector $\\mathbf{j}$ gives the vector $\\mathbf{b}$.\n", "\n", "Remember that we used the components of $\\mathbf{c}$ in a linear combination of $\\mathbf{a}$ and $\\mathbf{b}$ to get $\\mathbf{c}^\\prime$: $2\\,\\mathbf{a} + 1\\,\\mathbf{b}$.\n", "What we find is that the linear transformation represented by the matrix $A$, transforms the vector $\\mathbf{c}$ to the linear combination of the transformed $\\mathbf{i}$ and $\\mathbf{j}$.\n", "\n", "Since _all_ vectors are a linear combination of the basis vectors, $\\mathbf{i}$ and $\\mathbf{j}$, scaled by the vector components, they are _all_ transformed to a linear combination of $\\mathbf{a}$ and $\\mathbf{b}$ with the same scalars." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's try to visualize that. Our helpful custom function `plot_linear_transformation()` draws a grid of points on the plane, then applies the linear transformation described by the matrix argument, and plots the transformed grid. This is what $A$ does to the grid:" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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PW2+9hdvtDng9SgX2Ub/hhhvYtWtXQMu+Xt3J1/c0sfUDObgc1oBjiUTfeuccB2vO80TGMWyOZDLzl5GQmh3w+xophnSdD7xUzQdyE7h/SWqgTwvpm2DYHtFnBlfxxJwMCpKM/XBXtA/wzLuNYRFLuMUzVixPP/00r7+xkwTHIQD6+/s4fPgwc+fOJTExiUcffYQZM2aMuR1H9vIxlznb5aHmid8TP2dD2L8vsRxPOMUy0DZo6PZjzS15qfzomCJ9XjYd1Yc4c+g1EtNyyMhfSrxjmtHhBU1SnJmV6fFsr+0OSiL64osv0tPTw0033QRAb28vAPfffz/Tpk3jZz/7GYWFhWOup7o6sB2iGzZsCDi2G7I0rCbF27XdfLIoOeDnRaJbZqbwx9oBrHM2YGk4QtWxbVE5oTIpRYlTY1ttF19anBIWibZhiWgDiZi1FOyJEzodJmjMg3000BMWsYRbPGPF8sBXv8UDX/3WxdvDM/lnf/W7cc3k8xLTxlymt7WPQUwR8b7EcjzhFEv8YJ+h2481JS6Np460cKx/Gjcuv4P2prM0Vh7idOmLTMsoID1vMXHxCUaHGRQlLgc/ONxM58AQCdbJ7fl/8MEHefDBBy/eHh5Hn3rqqXGNozk5AZ0iOi4Oq4lVGfFsi4FE9LpMO3Emxe62OD6z+Ga6WutoOHPQN6HKJiN/WdRMqEpcGn8408GZjgEKkuKMDkeumhdCCDF5uQlWCpKsbK/tRilFckYes1ZuxDlrFZ2ttZTv20r96f0MDvQaHeqklbg0BnV4p77b6FBCzu3SOHC+l/Z+j9GhhJTdYmJ1pv3i5zch1UXB8jvImbeWvu42Tpe+SM3JXfT3dhod6qStyrCjWRTbasLj8yuJqAiK+++/n09+8pNX/V8IETvcLo0ddd14hrynrppMZlKz51C46m7SZyykta6c8r1baKo6ypBnwOBoJy5LszB3WlzQv8jDcRxd79QY0mFnXY/RoYSc26VxpLmPll5v0n31hKouKiZUcWbFDVka22rDIxGVq+ZFUDz11FNGhyCEMJjb5eA/T7Zx8HwvKzPsF+83W6ykz1xMinM256uO0XT2KC01p7z3ZRWiTJG3T6TEpfGr99sZ8OhYzcE5zy4cx9HpdgsLU21sq+3ijpnRcWrFaNa5NNQBeLuum035ly64HZ5QJWcW0FJzgvPVx7lQf5q0nPmk5czFZDb+WoHxKnFqPLivicbuQTI0Y1PByPvrF0IIEZbmpsSRYTezfZQ9LZa4eLIKV1K46i4SUpzUle+lfP8LtDVWYlQFl4lyuxx0DQ5R2hS5e8YC5XZpvFvfQ59nyOhQQirFZmZJWvyon9/hCVVR8SamZc2iqeooZXu30FL7PvpQZL03a5x2zMqbdBtNElEhhBBBYVKKEpf3kN+1Esu4+ASy565h1vIPYtOSOHdiJ2cOvkJna90URjs5hclWXJqFbbVdRocScm6XRo9HZ29DbCTdexp66B4YPbG0xMWTNSuyJ1RJcWZWpMeHxeF5SUSFEEIETYnTQV33IGVt/WMuG5+QwoyFN5K35FaUMnH2yJtUHnmDno7mKYh0cpRSuLM1ttd2MxQhycdE5SXFMSPBGhNJd4lLo39IZ3fD2OfEjjShqjgQORMqt8vB/sYeOq+RdE8FSUSFEEIEzYr0eBwW07j2tDimZZK39DZyF5Qw2NdDxYFXqD6+g77u9hBGOnlul0ZTr4eTrWMn3ZHOeyFaT9Qn3TkJVmYlWcf1+fWfUJlMkTOhCpfqD5KICiGECBqrWbEmyz7uK8qVUiRNz2XWyg/imrOanvYmTu9/gbqyPQz2h+cV20vS4kmymmJiT6E7W6Olz8PR5uivz1vi0thZ183g0PiS7kibUGWGqPrDeEkiKoQQIqjc2Rrvt/VT1zX+Ek1KmUjJKqRw1V1k5C+lreksZXs303jmEJ7B8NrzaDYp1rvCpwxOKC1MtZFqG/1CtGjidjloHxji0PnxnxM72oSqtmwPA33h9965XRo767vp9xi3p1sSUSGEEEG1JkvDophU0mIyW5ieu4Ci4k2kZs+l+dwJyvZuofncCYaGwqe4eolLo6J9gKqOyK2LGojhC9Hequ2KmAtyJmqer/rDZCYYl0+oltHedJbyfVvCbkJV4nLQPahT2mTcUQdJRIUQQgSVtzWkPSh7Cs2WODLzl1FYfDdJ03NpqDhA+b6tXKg/HRYJ0Wpfa8hY2FNY4tKo7hzkTJQn3SrA6g+B8E6o5l8xodocNhOqS9UfjPv8SiIqhBAi6ILdGtJq03DNXs2slRuxJ6RSc+pdTpe+SEfzOUMT0kutIaP/PNHiDDt2c2wk3W6Xg/oAqz8E4vIJ1cywmVANV39428DqD5KICiGECLr1rtC0hrRpSeQuKKFg2e1YrPFUHdtG5eHX6G5rDOp2xsPt0jjs1xoyWl1sDRkmPcpDafn0eBKs46v+EAjvhOo674QqMS0sJlTD1R9OGFT9QRJRIYQQQZdut7AgxRayK8rtSdOZufgWZi66iSHPIGcOvUbVsW30dl0IyfauZZ1LQynYEQZdakKtxKXxXmsfTT2DRocSUhOt/hAom5ZE7vz1YTGhWpIWT3KccdUfJBEVQggREu7s0LaGVEqRkOqiYPkd5MxbS19XK6dLX6Tm1DsM9E7dl+pYrSGjyVqnHZOCt2Pgtbpd3uoPtROo/hCocJhQmU2K9U7NsM+vJKJCCCFCYqpaQyqlSM7IY9aqu3DOWkVnSy1l+7ZQf7qUwYGpqXtZ4tLYPUZryGiQFGdmZZi0hgy1G7I0rFNwIdpVE6ruC94J1cmpm1AZWf1BElEhhBAhkZdondLWkCaTmdTsORSuupv0GQtprSujfO9mmqqOMuQJ7RfseFpDRroSl4N9YdAaMtS81R+mLum+OKFaudE7oWqdugnV6kw7NoMuRJNEVAghREgopQxpDWm2WEmfuZii4rtJziyg6exRyvZuoaX2ffSh0CRPuQlWCpKsMXF4PlxaQ04Ft0vj4Ple2vqm7kI0IyZU8RYT12XYDTlPVBJRIYQQIVPiMq41pCXOjrNwFYWr7iIhxUld+V7K979AW2NlSK5Q9ibd3XjG2Roy0mRpFuaEQWvIqbDO6av+YEDSfWlCtYlpmbNCPqFyuzSOGFD9QRJRIYQQIbMozfjWkHHxCWTPXcOs5XcQZ0/k3ImdnDn4Cp2tdUHdznBryIMTaA0ZadwujV31PQwY2BpyKqTbLSxMtRn6+bXExZNVuDLkEyqjqj9IIiqEECJkTMrbjz0cWkPGJ6Qyc9FN5C25FZSJs0fepPLIG/R0NAdl/cOtIWPh8Lzb5aBrcIjSpthIut8JYfWHQF2aUH0wJBOq4eoPU30hmiSiQgghQqrEGV6tIR3TMslfehu5C9Yz2NdNxYFXOHdiB3097ZNabzBbQ4a7S60ho7+jVIlLo9ejsyfE1R8CFZ+QcnFCpYI8oXK7NPZMcfUHSUSFEEKEVHFmfNi1hlRKkTR9BrNW3olr9mq625o4ve8F6sr2MNg/8SvfS5wO6oLYGjJcXWwNWWdca8ipMlz9IdzauDqmZZK39DZyF5Qw2NdDxYFXqD6+g77uiU+ojKj+IImoEEKIkLKZTVwfwi41k6GUiRRnIYWr7iIjfyltjWcp27uZxjOH8AyOP5lckR6PwxL81pDhyO3SaOzxcNKg1pBTZbj6w9tTXP0hEN4JVS6zVn4Q1+zV9LQ3cXr/xCdUOQlWZiVZp/TzK4moEEKIkHO7HGHdGtJktjA9dwFFxXeT6prD+XPHKdu7heZzJxgaCvwqYqtZsdYZnkl3sC1JiyfJalxryKnkztZo7fNwxIDqD4G4akLVNPEJldvlYOcUVn+QRFQIIUTIRUprSLPVRmbBcoqKN5E0PZeGigOU79vKhfrTAZ/3WeJrDVkXwtaQ4cBs8l6IFgt7fxemGl/9IRAXJ1Sr7iY1e+6EJlQlLm1Kqz9IIiqEECLkkuLMLJ8eOa0hrTYN1+zVzFp5J/aEVGpOvcvp0hfpaD43ZkK6JkvDogj7pCUY3L7WkNWd0Z10D1d/2BYG1R8CYbbayMxfNqEJ1XD1h6n6W5VEVAghxJRwuzT2NfbQFUGtIW1aMrkLSshfdjsWazxVx7ZRefg1utuaRn2OtzWkPWKS7sm4LtNO3BT0Yw8Hbld4VX8IxKUJ1caAJ1TD1R+2T1H1B0lEhRBCTInh1pC7IrA1pJY0nZmLb2HGohsZ8gxy5tCrVB3bRm/XhRGXd7s0Dpzvpb1/arvUTDW7xcTqTDvbaqL/PNHiDDt2s4rI839tWtIoE6rGEZd3u6au+oMkomJStmzZwp133smtt97K2rVrWbFiBb/73e+MDksIEYacDiuzkyO3NaRSisTUbAqW30HOvDX0dbVSUfoSNafeYaD38kRsvcvXGrJu7CuXI30cdbs0DhvQGnKqxZmVt/pDBO/9vXpC9dqIE6rl0+NJsE5N9QdJRMWkPP3003z84x/n9ddfZ+fOnTz00EN86lOf4ujRo0aHJoQIQ+7syG8NqZQiOSOfWavuInPWCjqbayjbt4X606UMDnivqk63W1iQYgvoivJIH0eHW0PunOLWkEZwuxwcb+2jsTs8qz8EIpAJldWsWDNFJdckERWT8t3vfpd77rnn4m23283Q0BDl5eUGRiWECFdulxY1rSFNJjNp2XMpLN7E9NyFtNaVUb53M01VRxnyDODO1ng3gNaQkT6OGtUa0ggXqz9EQdLtP6HKmrXyqgmV21f9IdQsId+CiGorVqy4+P+BgQGefPJJ5s+fz6233hrwOs6dOzfmMvUd0X3IR4hYUZQch9PXGnJ1lt3ocILCbLGSkbeYVFcRTVXHaDp7lJaaUyydvoieQSt7G3pZ59JGff5UjaOhVOLS+NGxVnoGh7BboncfV1KcmRW+6g8fnZVkdDhBYTKZSc2eQ3JmAc3nTtB87jgX6suZ55yHZnKEfPuGJaKZdODpbqXHYjUqBAA83QNhE0u4xTOeWB555BFeeOEFCgsLeWnL85j1Pno6Aiv8u3b18rEXmp6DhaGIe19iLZ7erkGGPIP0dl2gx2LsPLe3axBSMg2NQVxtuEvNmzVdfFXXMSlldEhBY4mz4yxcRVr2XBrPHmGgdh+pg7N5tczDWmchaozX+vnPf55f//rXLFiwgFdffZWEhISAt52bmxvQcvPmzQt4neNR4tJ46kgLuxt6uDE79MmLkdzZDn5wuJnOgSESrNGTdF85oWqtOcbfxwPMCul2lVH1sH6/+ed6fpKVeLOxv8RezxBn2gcIh1jCLZ7xx6JTW1tLc3Mzc+fOw2oNLCkqLd0/9kIWG9948jm2/OKxCHxfYieeij4bX6vJ57HsMxTYjO1AUtFnY+OGj0VPljOyiDzRsrSph7/eXs8vb3IxP9VmdDgh09vZwmO73ufVBsVzC1rIKlhKQorzms/xeDw8/PDD/OIXv2D37t04nddefthYSe6wefPmcfz48YCWHa9PvHaOudNsPFycHpL1h4v67kHufLma712XzobcwCcLkaa/t5O3D+7llutvCuk4atgui2cGV/HEnAwKkozdg1PRPsAz7zaGRSzhFs9EYslfpnPzzTfzgQ+Y+MpXvhLQcxzZY+8RPdvloe2J3xM/Z0NEvi+xEs9A2yC21nZy56+nINnYPaIDbZF7MUG0W+rXGjKaE9H4hFQ+tGIpW9+s4lRPJ31H3iQhJYuM/GXYE9NGfI7ZbOahhx7i2Wef5fvf/z5PPvlkQNuqrq4OaLkNGzYEHP94lbg0fn+6A8+QjtkUvXPALM3CnGne6g/RnIjGxSewdOn6kG/HsG+KBhIxaynYE40dhMyDfTTQExaxhFs8gcTS399PXFzcZfdpSdPZU3p01IH2SnkBLNfb2scgpoh5X2I1nvjBPkzmbuId08IiFhGezCbFOqe3NeTfLkw1OpyQWpRmY7oWT3nSUta5img8c4iKA6+QnDGT9Lwl2OxJV42jJpOJoqKice25zMnJCUX44+J2OfjPk20cau5lRXp0nP87GrdL47n32+j36MSZozfpnm4PfZpo/HFFEdGWL796b2ZdXR0ul8uAaIQQkaIk5lpDdpOYlsuslXfimn0d3W1NnN73AnVxk0giAAAgAElEQVRle1m35vqrnheJ4+jF1pARWid2PEpcGt2DOqVNY9eJFdcmiaiYlOPHj/PSSy9dvP2rX/2KU6dO8dnPftbAqIQQ4e76rNhpDVnivNQaUikTKc4iClfdRUb+UtoaK/mrj1zPn174FZ5Bb1IeqePoVLeGNFJRchwuzRITn99Qk/JNYlL+9V//le9+97s89thjeDwelFJs3bqVtWvXGh2aECKM+beG/PTsZKPDCanizHjsZm/SXZDkPQRvMluYnruAlKxCjpbVcr76OL99+kF2Hz7D4VM1ETuOul0Onj/dQVlbP7OnGX/qUqgopXBna7xe3cVXl0VX9YepJomomJQvfvGLfPGLXzQ6DCFEBCpxaTxaep6WXg+p8WajwwkZm9nkbQ1Z0819c6dd9pjZauNj997PQF83TWePsGzJaSw2jYy8eei6HvDV8OFi+fR4HBZva8hoTkTB+/n9TVk7J1r7WRDFF92FmhyaF0IIYYh1Tm+R91hpDfleax9NPSNXc7DaNFyzVzNr5Z3YE1KpOfkOp0tfpKP5XEQd5raaFWud9pg4ZD1c/WF7AG1cxegkERVCCGGI1HgzS9JssdUacozXatOSyV1QQv6y27BYbVQd20bl4dfobmuaokgnz+3SOHWhn7qu6L4QzWy6dCGamDhJRIUQQhimxOVgd0MPPYPX7sce6ZLizCyfHng/di0pnZmLb2XGohsZ8gxy5tCrVB3bRm/XhRBHOnk3ZGlYFDGxV3S4+kNVR3Qn3aEkiagQQgjDlLg0+od0djdEfxkct0tjX2MPXQOBJd1KKRJTsylYfgfZc9fQ19VKRelL1Jx6l4He8D0c7LCaKM6MjcPzqzNjp/pDqEgiKoQQwjAzEq0UJFljpvbkoA676sf3WpVSTMvMZ9aqu8ictYLO5nOU7dtC/elSBgfCs3GD26VRer6X9n6P0aGE1MXqD3Ke6IRJIiqEEMJQbpfGjrpuPEORc1HORDgdVmYnx0046TaZzKRlz6WweBPTcxfSWldG+d7NNFUdY8gTXi1t1zk1hnTYWRcbe7qPNPfR0hvdSXeoSCIqhBDCUG6Xg/aBIQ419xodSsi5szV21fcw4Jl40m22WMnIW0xR8d0kZxbQdPYIZXu30FJbhj4UHufaptstLEy1xcSewnUuDaVgRwxUfwgFSUSFEEIYam5KHOnxsdEa0u3S6BocorRp8km3Jc6Os3AVhSs34kjJoq58D+X7X6Ct6WxYlHwqcWm8W99D/ySS7kiQYjOzODU2qj+EgiSiQgghDGWKsdaQTs0S1D2FcfZEcuauYdbyO4izJ3Lu+A7OHPwjna31QdvGRLhdGj0enb2NMXB4PtvBnoYeugO8EE1cIomoEEIIw7ldDmq7Bylr6zc6lJBSSuF2abxd181QkJPu+IRUZi66ibwltwJw9sgbnD3yJj2dLUHdTqDyEq3MSLDGxJ7CWKr+EGySiAohhDDcivRLrSGjnTtbo7HHw8nW0CTdjmmZ5C+7ndz56xno66Ki9GXOndhBf09HSLY3motJd23wk+5wk5vgq/4QA5/fYJNEVAghhOGsZsWarNioPTncGjKUF/IopUhKn8GslXfimn0d3W2NlO/bymB/D4P9U7fXzp2t0dLn4VhLeJaZCia3S2NnDFR/CDZJRIUQQoQFd3bstIZc55ya1pBKmUhxFlG46m4y8pYy5BmgbO8WGs8cwjMY+vd5YaqNVFusXIjmrf5w8Hz0V38IJklEhRBChIU1MdQa0p3tbQ1Z3Tk1SbfJbGH6jAXExSeS6prN+XPHKd+7meZzJxgaCl39S5O61I892i9Em5cSR4bdLIfnx0kSUSGEEGHBYTWxKiM2Ds8b1hpSKTILllNUvInEtBwaKg5Qvm8rFxoqQpYoul0aVZ0DVEZ5P3YVQ9UfgkkSUSGEEGGjJNZaQ9YYU/DdatNwzbmeWSvuxJ6QSs3Jd6gofYmO5nNBT6KKM+zYzSom9hSWOB3UxUD1h2CSRFQIIUTYWB9DrSFLXBqHDW4NaXMkk7ughPxlt2G2xlF1bBuVh1+nu60paNuIMyuuj5EL0WKp+kOwSCIqhBAibGRoFhakxEhrSKcGwM4waA2pJaUzc/GtzFh0I0Oefs4cepWqY9vo7boQlPW7XQ6OtfTR1DMYlPWFK6tZsdZpj4mLs4JFElEhhBBhJVZaQ6bGm1mSFj6tIZVSJKZmU7D8g2TPvYG+rlYqSl+i5tS7DPRObmKw1mnHpODtMHmtoVTi0ni/rZ/aKK/+ECySiAohhAgr7uzYaQ1Z4nKwu6GHnsHwaQ2plGJaZgGzVt1F5qwVdDafo2zfFuorDuAZmFg90KQ4Myumx7M9DPb+htpw9YdYSLqDQRJRIYQQYSVfWkOGBZPJTFr2XAqLNzE9dyGtte9TtnczTVXHGPKM/xC7O9vB3oYeuqK8H7vDaqI40x4Tn99gkERUCCFEWBkugxMLrSFnJPpaQ4bxOYVmi5WMvMUUFd9NckY+TWePULZ3Cy21ZehDgSeV6512BnXYVR++rzVYSpwaB2Kg+kMwSCIqhBAi7LhdsdUackcEtIa0xNlxFhVTuHIjjmmZ1JXtoXz/C7Q3nQ2o5JPTYWXOtLiYuHp+vSt2qj9MliSiQgghws6iNBspMdYa8lBzZLSGjLMnkjNvLQUr7iDOnkD18R2cOfhHOlvrx3yutx97DwNRfiFauj12qj9MliSiQgghwo5JKdY77THRGnLucGvICEu67QmpzFx0M3lLbgHg7JE3OHvkTXo6W0Z9TolLo2twiNKmyEi6J8Od7a3+0OeJ7nNiJ0sSUSGEEGHJ7XLERGtIb9Idua0hHdOyyF92O7nz19Pf20lF6cucO7GT/p6Oq5YtSo7DpVnYXhf9ewrdLl/1h4boT7onQxJRMWm/+93v2LBhAzfffDOrVq3iIx/5CBUVFUaHJYSIcMWZ8cTHSGvIwRPvsu3QcW7YdE9EjqNKKZLSZ1C4aiOu2dfRdaGB8n1bqSvby2B/z2XLxUo/9ryL1R+iP+meDElExaR9+tOf5stf/jJvvvkme/bsITExkdtvv53eXpkFChFKrX3RfUWuzWzihhhpDfnwX36CPGcGf/FPP4rocVQpEynOIoqK7yYjbwltjWco27uFxsrDeAa9e7bd2RqNPR5OtEZ3P3allO9CtJ6or/4wGZKIikm7++672bBhAwAmk4kvfOELlJWVceDAAYMjEyK67YiBBC1WWkNu2vhB7pyXzbba7qgYR01mC9NnLKSoeBOprtmcr36P8r2baT53gsUpVpKsppjYU+jO9lZ/ONoc/dUfJspidAAi8j3//POX3Y6Pjwegvz+w2e65c+fGXKa+I7r3/AgxEW/VdnFXfqLRYYSUf2vIj8xKMjqckHn++ed5rbqTb+xpoq5rICTjqBHMVhuZBctJzZ5LU+VhGioO0FJzklVJC9hWY+ZvF6YaHWJILUy1kWozs622myXT440OJywZlohm0oGnu5Uei9WoEADwdA+ETSzhFs9EYzmwdyerli1gxZJ59HQ0j7n82tXLx17p9BwsDEX0+xIqvV2DDHkG6e26QI/F2LlluMVCSqahMYTa22fqaZ5rIi0tw+hQQiYpzsxyX2vIaE5Ewa81ZF0P7e++i8vlYs2aNQE9Nzc3N6Dl5s2bN5kQJ8xq03DNuZ60nPk0VB5kbvNxXm6ayYnqIebm5KKUMiSuUDMpxXqXxrbaLv5uUUrUvs7JMOyb4j7LPnpPWakwG3t2QK9niPssA2ERS7jFM5FYdH0IW08l3//Hv6bqyOsBPec7D9wz9kIWG9948jl6T70Wke9LKFX32ejrzqf6+CGsNmMP/4RbLEtzPmZoDKHW79HZuucdbp45jcy8ZdgcyUaHFBJul8ZTR1roGhjCYTX+by5UHFYTqzLsvFndzrYnn+Tf/u3fsFqNn+wGk82RzIwFbu7KauQ/Xqlly4Fj2FtOkpG/DC0p3ejwQsLt0th8poMzHQMUJMUZHU7YMSwRfWZwFU/MyaAgydg/sor2AZ55tzEsYgm3eCYSy9e//g0yMtK5688DSC59HNlj7xE92+Wh7YnfEz9nQ0S+L6E00DaIrbWd3PnrKUg2di9kuMUS7eZlpXMqzsGazvc4XfoiyZkFZMxcjDXeYXRoQVXi0vjnwy3squ9mQ26C0eGElNul8dd/2MdnP/YpPvKRjwT8vOrq6oCWGz6f32hpaRmszx/iREcCnoGTnDn4KonTc6JyQlWcYcduVmyr6ZZEdASGfVM0kIhZS8GeaDMqBADMg3000BMWsYRbPOON5Wtf+xqdvR5+8OAj4zr8kJeYNuYyva19DGKKyPcl1OIH+zCZu4l3TDM8nnCLJdq5szX+p8LDI+s20l5fxvmqY7Q1niE1ey7puQswW43/fAaD02FldrK3NWS0J6Lbf/4vqFQ3N/3Vl8f1vJycnBBFFDo3uhw8eqCHaSW3Y26vorHycFROqOLMiut91R/+Yt40o8MJO9F7jENMqccff5zKykp+8pOfoJSitLSU0tJSo8MSIqqVuBy09Q9xtHWAtJx5FBZvYnruAlpr36ds72bOVx1jyBMde4bd2dHfGvLxxx+nseIUH1g2m+113VE/jq5zaQDsqu9hWmYBhavuIrNgOZ3N5yjbt4X6igN4BqJjQul2OXivNfqrP0yEJKJi0n784x/z3HPP8aUvfYkDBw6wf/9+XnjhBY4ePWp0aEJEtXkpcaTHmy8WfDdbrGTkLaGo+G6SM/JprDxM+b4ttNSWoeuR3WbQ7WsNeeB8ZNXVDJT/OJrX38Tr5U1sfuGlqB5HU2xmFqfaLn5+TSZz1E6o/Ks/iMtJ+SYxKR0dHXz+859naGiIG2644bLHnnnmGYOiEiI2mHxdarbVdPP/LU69eEqMJc6Os6iYtJx5NFYepq5sD83njpOZv4zE6ZF5hXJRchxOzcK22i6uy7QbHU5QXTWOpuXA//k+h36/hWe+9UWjwwspd7aDHx1rpWdwCLvFu29seEKV6ppN09mjNFYepqX2FNNnLCbFOQulIm8fWlKcmRXT49kW5WXIJiLyfpsirCQmJuLxeNB1/aqfe++91+jwhIh6JS6N2u5Bytuu7sceZ08kZ95aClbcQZw9gerjb3Pm4B/pulBvQKSTE82tIa8cR4eaqviQ+3oe+e9Xo34cLXFp9A/p7G7oueqx4QlV4aq70JIzqSvbQ/m+F2hvqorIz0CJS2NfYw+dA5F9dCLYJBEVQogItjLdjsNiYvs1utTYE1KZuehm8pbcAkDl4Tc4e/RNejpbpirMoHC7Yqc1ZIlL4+3a7qhvDZmbYKUgyXrNNq7RMqEqcWkM6vBOvRye9yeJqBBCRDCrWbEmy37xPLtrcUzLIn/Z7eTOX0d/TycVpS9z7sRO+ns6piDSyVs2PT52WkO6vK0hj7VEx8U61+L2Jd2eoWsn3ZE+oXI6rMyZFse2GklE/UkiKoQQEc6drXHyQj/13WNf0KGUIil9JoUrN+Isuo6uCw2U73+BurK9DPZffXg0nJhNirVOLaCkO9ItSvO1hoyBpMXtctA+MMSh5sAuRIvkCVWJS2NXfXRXfxgvSUSFECLC3TDcGnIcCZoymUh1FVFUfDcZMxfT1niGsr1baKw8jGfw6vNNw4XbpVHRPkB1Z/jGGAwmpVjn9O7pjsTzIcdjbkocGXbzNQ/PX2nECdW+rWE/oRqu/lDaFJ3VHyZCElEhhIhwCVYTKzPsEzpkbTJbmD5jIUXFm0hxzeZ89XuU791M87kTDA15QhDt5KzOtBNnUuNKWiKV2+WgqnOAyo7oT7qHqz+MN+m+bEKVtyTsJ1T+1R+ElySiQggRBdwujf1NvbT3Tyx5NFttZBUsp2jV3SSk5dBQcYDT+7ZyoaEirPbIaVYT12XaYyIRLc6M97aGjIHXWuJ0UNs9SFnbxC5Ei5QJlVLKe05sXfRfiBYoSUSFECIKrHdqDOmwq25yhyWt8Q6y51xPwYoPYktIoebkO1QceImO5pqwSUjdLo3Dzb209IZPghEKNrPpYmvIaLciPd5X/WFyrzUSJlTubG/1h5NRXv0hUJKICiFEFMjQLMxPsQVt71m8YxozFrjJX3obJnMcVcfe4uyR1+lubwrK+idjnVND12FnXfQnaG6Xg2Mt0d8acjzVHwJaXxhPqJamxU71h0BIIiqEEFHC7dJ4t6Gb/iBekaslp5O35FZmLHTjGejnzMFXqX5vO31dbUHbxnilxptZnBa8pDucDbeG3BELSXe2xqkAqz8EKhwnVGaTYl2MVH8IhCSiQggRJdzZGt2DOvsag3vVsFKKxLQcClZ8kOy5N9DT2cLp0hepPfUuA33GfJm6XQ52N/TQMxjdXWqS4sws97WGjHZrfNUfQnEqQrhNqNzZ3uoPVVF+IVogJBEVQogokZ9oJTfBErKkRSnFtMwCClfdRWbBctqbz1G2dzMNFQfwDExt4fVrtYaMNm6Xxt6GHrqivDWkw2piVYadbTWhOWQdThOqWKr+MBZJRIUQIkp4r8h1sD3ErSFNJjNpOfMoKt7E9NwFtNS+T9neLZyveo8hz9ScyzgjcezWkNEillpDul0apecnXv0hEFdOqDoMmFDZLSZWZ9qv2Zo3VkgiKoQQUWQqW0OaLVYy8pZQVHw3yRl5NFYeonzfFlrrytD10O+9C7Q1ZKRzOqzMTo6LicPz613e6g87J1n9IRDDE6rCqyZUx6ZkQuWt/tAX9dUfxiKJqBBCRJFFaTZSprg1pCXOjrOomFmrNqIlZ1D7/h5O73+R9qaqkF6hXDLO1pCRzJ2tsbMu+ltDptstLEixTekV5VdPqA5PyYRqrVMDYuNCtGuRRFQIIaKISSnWO42pPWmzJ5Ezbx0Fyz+A1eag+vjbnDn4R7ou1Idke/NS4kiPH19ryEg13BrywPnYSLrfre8JavWHQEz1hCo13sySNFtMfH6vRRJRIYSIMiUuB2c7B6hsN6Zgtj0xjZmLb2bm4lsAqDz8BmeP/onezpagbsekFOsn2Boy0sRSa8gSl0aPR2dvkKs/BGoqJ1QlMVL94VokERVCiChzXWY88Wbjr8hNSMkif9nt5MxfR39PB6dLX+bciZ3093QEbRtul0Zt9yDlbdFdBme4NeT22uhPuvMTrcxIMP5CtJEnVG8GdUIVS9UfRiOJqBBCRBmb2cQNQexSMxlKKZLTZ1K4ciPOouvoutBA+f4XqCvby2D/5L98V6bbcVhio0tNicvbGvJElLeG9E+6w6Ef+/CEKnf+Ovp7OoM6oRqu/jCV53SHG0lEhRAiCpW4NI629HE+TFpDKpOJVFcRRcV3kz5zMW2NZyjbu4XGyiN4Bie+NzPYrSHD2bLpsdMasmQKqz8EQilFUogmVG6Xxo666K/+MBpJRIUQIgqtzdIwKXg7zK7INZktpM9YSGHxJlJcszlffYzyvZtprjnJ0NDEytiEojVkOBpuDWn0IeupsCjNRuoUV38IRCgmVO4Yqv4wEklEhRAiCiXbwrs1pMVqI6tgOUWr7iYhLYeG06Wc3reVCw1nxn0O5A0hbA0ZbkpcGqfbB6jujO5zYi9eiBam58QGc0I1NyWODHv4Jd1TRRJRIYSIUiUujX2NvXSHcWtIa7yD7DnXU7Dig9gcKdSc3EXFgZfpaKkJOAFJsJpYGcLWkOHk+qzYaQ1Z4tSo6hygMoz7sY8+oaoI+PPrLbkWvkl3qEkiKoQQUarEpTEwpPNOBFyRG++YxoyFbvKX3obJbKXq6FucPfI63e1NAT1/KlpDhgO7xcR1mcbUiZ1qxZnx2MOg+kMgrp5QvUPFgZfoaA5sQuV2OajrHqSsLbovRBuJJKJCCBGlXMOtISNoT6GWnE7ekluZsdDN4EAfZw6+SvV72+nrbrvm89Y7p641pNG8rSF7ae2L7qTbZjZxfYRdiHb5hCqOqmOBTahWpMf7qj9EzmsNFklEhRAiirmzNXbW9zAYQVfkKqVITMth1oo7yZ57Az2dLZze/yK17+9moG/kL+oMzcL8lNjoUrPOqaHrsCMGXqvb5eBYGFV/CNR4J1TD1R9i4fN7JUlERVD09/fz9a9/HYvFQmVlpdHhCCF83C6NzoEhDjRF3hW5SimmZRZQuOouMguW036+mrK9m2moOIBn4OqyPm6Xxjv13VPeGjJYAh1HU+PNLE6zxcTes7VOe1hWfwjEqBOqU++OOKEarv5Q1xW+58SGgiSiYtIqKyspKSmhtrYWjye6DxUJEWkutYaMvC/yYSaTmbSceRQV3830nPm01J6ibO8Wzle9x5Dn0p4yd7axrSEnY7zjqDtGWkMmxYV39YdAXDWhaj434oRqTQxVf/AniaiYtM7OTp577jnuu+8+o0MRQlxBKUWJS2NbbVfEX5FrtsSRkb+UouJNJGfk0Vh5iPJ9W2itK0PXh8hPtJKbYInIL/LxjqPDrSH3RMCFaJPl9lV/6Arj6g+BuDSh2sT03AW01L5/2YTKYTWxKiP2Ds9LIiombeHChRQWFhodhhBiFG5fa8iTF6LjilxLnB1nUTGzVm1ES86g9v09nN7/Ih3nqylxhk9ryPEY7zh6sTVkDCQtF6s/1EfHazVbrGTkLaGo+O6rJlRuZ3xMVH/wZzE6ACHOnTs35jL1HbHzRylEsF1sDVnTzbwUm9HhBI3NnkTOvHWk5cyn8cxBqo+/TaHZyfnuXI619LE4Ld7oEEPK7dL4/ekOPEM6dbU1RocTMs7h6g+13dyam2B0OEEzPKFKzZlLU+Vhat/fw1xbAkU42Vk7nTvyEo0OcUoYlohm0oGnu5Uei9WoEADwdA+ETSzhFs94Y1GeXmZmpzPY205PR3PA21m7evnYC03PwcJQWLwvvV2DDHkG6e26QI/F+LlcOMUTbrGQkmloDOHCbFKsdWpsr+vmcwtTjA4n6OyJacxcfAudrXXYKg5h62vlv3Y3UrR+PvbEVKPDCxm3y8F/nmzjcHMvK3JzA3rOvHnzQhxVaLizNX5T1s6AR8dqVkaHE1SXT6gOcY/tOF2naumadgOOadE/hhn2TXGfZR+9p6xUmI09O6DXM8R9loGwiCXc4hlvLLaeDr7zwD10VO+jouFIwNv5zgP3jLmM2WrjH554jt5Trxn+vlT32ejrzqf6+CGstquv3I3leMItlqU5HzM0hnDidmm8XNXJuc4BchKMn3SHQkKKk1nLs7ip8zRvn23gf17+CXVmG30pM1iYM4uVzplkJ05DqehIZOamxJEeb46Jw/Nul8ZPjl/gwPlersu0Gx1OSHgnVDfzrqeMlrOHOHP4NRJTs8nMX0p8QvROqAxLRJ8ZXMUTczIoSDJ2QKxoH+CZdxvDIpZwi2e8sezdu49//P63eeONN8jOzg54O47ssfeInt12iAsDvyV+zgbD35eBtkFsre3kzl9PQbLxe0TDKZ5wi0VcsjrzUmvIP5udbHQ4IaOU4rYiF682muhIX0p8zT7SGk/wP+X7+GxLO/b4BFY6Z7LSOYOVrpmsdM4kKyEy3w/T8IVoNd1UVVUFlGBv2LBhCiILvkvVH7qiNhEdVjxrJh8/bWZJ5iC29hOcLn2Z5Mx8MvKWEBcfPacmDDPsm6KBRMxaCvZEY89XMg/20UBPWMQSbvGMNxbdHM/ZmiYs8UnYE9MC3k5eAMvW/+tWBj06JrMDe6Kx583ED/ZhMncT75hm+O8o3OIJt1jEJZr1UmvIaE5EAa7LjCfeYsKetRrztER+v2sLd6Qksi4xgVcutPPK6WO8VH704vLZidN8yelMVrpmsiJrBumOyDg/z+1y8PuKDnoTsymaFmd0OCGjlMLt0nizpouvLtWjZq/2SPITrcxIiOOtriS+uXIjrfWnaTp7hPKms6Q4i0ifsRBLXPQk48YfixZiDHr/AH17DwPQd/A9g6MRInKVuDQONfdyIRZaQ2Z6W0N+ZukaPrruw3y5sp632ju5MyWJf85zcUtyAmbf8jUdF9jy/mEe3L6VD/zXv5Pxg6/wFy/8koEIqIt8qTVk5LRxnagSX/WHE63RUf1hNMMl196u7UZXilRXEUXFd5E+cxFtDRWU7d1CY+URPIPRUfheElExaf39/bjdbu6//34APvnJT/KxjwXv3Ly+dw+gd3tr5fW9cyBo6xUi1qwfbg0ZgV1qxsudrV1sDfmZxat5euOf87vmNv7hbB2Hunr4s/QUHs9zcn2ihv++NavJzJM3f5if3flprGbzqOsPtomOo7HUGnK4+kMsvFa3S6Olz8OxFu+RHZPZSvqMRRQWbyLFWcT56mOU791Mc81JhobCf8J0Lcaf4CYiXlxcHNu2bQvZ+ntf33nx/33vHEDXo/uwjBCh4t8acmOUl4ZZm6VdbA354YIkPr3oOhTw51uf5eeNLbxyoZ2Pp03jbzLTuGNaEr9rvsDR7l6+vPpWHlh9CyY1tftpJjOOurM1vrGnifruQbK06P1aN5sU65ze5gzRWP3B36I0G6k2M9tqui8rQ2ax2siatYK07Lk0nj1Cw+lSWs6dID1vKckZeRH53Sh7REVY03Wdnjd2Xbw91HiegePlBkYkRGQrcWnsbuihN8pbQybbzCy7ojXkny26jufuvg+TUtT2D/JU3XkePddArz7El13pfC07g/8u/ROrfv4Yr1ccNzD68bkhhlpDlrg0TrcPcK4zOg5Lj8akFOuc3tNLRuqIZo13kD3negpWfBCbI4Wak7uoOPAyHS01EddBTRJREdYG3z+Dp6r2svt6X99hUDRCRD63y0GfR2dPBPZjH6+RWkPes7D4YjIKUNbbz3fPNfJUXRNJZhPfzs1kDV189vkfccuvnmJ/7Vmjwg9YwsXWkNF/nuj1WZeqP0Q7t8tBVecAlR2jJ93xjmnMWOgmf+ltmMxWqo6+xdkjr9Pdfn4KI50cSURFWOt5befV971+9X1CiMBcbA1ZE/1f5KO1hrxnYWDb+6kAACAASURBVDG/uvsvLiajALZpTn5wvpOfNrSQH2/jezOdzOxuYMMvnuDj//MTyloapjr8cSlxaexviv7WkHaLidW+C9GiXXFmPHazCui1asnp5C25lRkL3QwO9HHm4B+pfm87fd1tUxDp5EgiKsLaSHs/Bw4ex9MUeOcmIcTlSlwab9d14xmKrEN44+Xyaw15pU8tXMWvN11KRu+evYTTn3+Um5e6ebimmd+ev8AKh8aTeU5U42lW/L/v8LmXf0NdR3h+sa93agzpsLMu+vd0l7g0Djf30hoL1R+y7AFPGpVSJKblMGvFnWTPvYGezhZO73+R2vd3M9AXvom7JKIibHmaW+kvPTbiY71vvDPF0QgRPdwuB239Qxxu7jU6lJBzZ2vsqu9hwHN10v3JBav4zaa/xKxM2CwWEm3xPFSykVOff4SiwhV8vbqBV1o7uGVaIo/PzKKq4iDznn6Qb761mbbe8Er4MjQLC1JsMXHIet1w9YcYeK1ul4P3Wvto6gm8QYdSimmZBRSuuovMguW0n6+mbO9mGioO4BkIv/rKkoiKsNX75jswyknXcnheiImblxLH9BhpDVni1OgcGOLA+ZGT7k8sWMlvPvQXOKyXGjBkJiTx77d/koN//W1sztl8pbKW3R3dfHT6NB5yTWfn0R0U/vBb/Mvu1+kNo1qOJS6Nd+q76R8h6Y4m/tUfot1ap91b/WECr9VkMpOWM4+i4ruZnjOfltpTlO3dwvnq9xjyhE/nOUlERdjq9bta/kp92/eg94bfzE6ISDDcGnL7KFfkRpPZ0+LI0izX3FP48fkruXfJ9VfdX5CSzq8/9Je8dd/XaEh08rWzdbzf28dfZqTy9+mJ/Ne7LzP7R//Is4ffwTNkfBUCd7ZGj0dnX0xciOZgT2P0V39IijOzfHo82ydR+9dsiSMjfylFxZtIzsij8cwhyvdtpbWuDF03/v2TRFSEJb1/gN5tu0d/vKeXvneluL0QE+V2adR0DXK6PXz26IXCcGvIbbVd10y648yj199cljWDP97zd/z2E1+k1JTIt6vraRn08HfO6dybFMdjb/w3S376KFvfP2xoYu9tDWmNiT2FJS6NPo/O7oZYSLo19jb0XFb9YSIscXacRcXMWrURLTmd2vf3cHr/i7SfrzL0cyuJqAhLfe8eQO+89mA60hX1QojArEi3o1kU22qiv+RPsFpD3pg3h933/QP/fOd9bOk18XhNI2YF38jO4HbrAF/c/DPW/eKf2VllTK1j5beneyjK93RfrP4QI0n3oA676oPzWm32JHLmraNg+Qew2hxUv/c2lYdepeuCMZUhJBEVYan39Z2Y0lJIfvCLOO776MX7zTlZpP3yX7AumUfv6zuj/rCiEKESZ1aszdImdcgvUgSzNaRSio/MW857f/OP3H/jR/nphV5+WN9MptXCd2ZksWCglQ/95gds/O8fcqyxJgjRj8+VrSGjmdulsSMGqj84fdUfgn0hmj0xjZmLb2bm4pvRdZ3Kw69z9uif6O1sCep2xiKJqAhLcdctJWvPH0j83J9h0uyXHlAK+y1ryHj5P5n22FcZam03LkghIpw7W+NEaz8N3eFz4UIoWEyKtb7WkMFbp5m/Wr6O9//2ET5cfBv/VH+BXzS2slCL5/GZTpJbq1nz8+9x79ZnOXth6srNLUqzkeJrDRntYq36w866kas/TFZCipP8ZbeTM38d/T0dnD7wMudO7qK/tzPo2xqJJKIiLGkbb748Ab2C8iWk5tTkKYxKiOgSS60h3SFqDalZ4/iHG26j/AuPsnLB9XyzuonNLe2sS3Lw5EwnbeeOs+jHD/HA689zvjv0X+wmpVjvjI2C73NT4kiPkeoPbpdG1+AQpU2hSbqVUiSnz6Rw5UachdfR1VpP+b6t1JXvC8n2/EkiKoQQMSrBamJlhj2oewrD1erM0LaGTLU7eOLmj3D8b79DxsxFfOVsPdvaO9mYksT3cjM4enIPs3/4LR7d8TJd/aE9bH6xNWT75M6JDXfD1R+21UR/9Yei5DicmoXtdaH9W1UmE6muIoqK7yJ95iLaGipCuj2QRFQIIWJaiUujtKmXjihvDalZTVw3Ba0hc5JS+Nmdn2HPX32LnrSZfPVsHYe7evh0egrfyErhpdI3KPrRgzxdup0BT2je8+LMeOIDbA0Z6dwuB7Xdg5S3xUb1h6kquWYyW0mfsYjC4k2h31bItyCEECJslTg1PDrsqo/+MjhT2Rpy3nQn//uxz/HCp/+e9+PT+GZVPTX9A3wuK42/TdF4evv/Mv/HD/Hf7+1nKMi1HG1mEzdk2WPilIsV6fE4LCa2x8Be/WBVfxgPi1+jh1CRRFQIIWJYhmZhfkpsdKlZb0BryOtzCtj2mQf4yYf/L3/y2Hj0XAN9+hBfdqXzUU3xjZd/yaqfP8YbFSeCul23y8HRlj7Oj6M1ZCSymhVrsmLjnNjh6g/RdiqNJKJCCBHj3DHUGnKRAa0hlVLcUbiIg3/1Tf7xtj/juY5BnqprIsls4tu5mayhi888/0Nu/fVTlNadDco2L7aGjIHyXO5sjZMX+qmP8uoP5ovVH6LrdyqJqBBCxDh3tkb3oM7+pug/PO92aYa1hjQpE59edB2nPvcwn12zkR+c7+SnDS3kx9v4p5lOcrsauPXZJ/jEH35KWcvkiosPt4aMtqRlJMPVHybSjz3SuF0aFe0DVAe5+oORJBEVQogYl59oJTfBEjO1J41uDWmzWPlS8c2Uf/4Rblrq5uGaZn57/gKrEjSezHNCQzkrf/IdPvfyb6jraJvwdtwujX2NvZNuDRnuEqwmVsVI9Yfrs0Jb/cEIkogKIUSMU0pR4nSwvS42WkPmJ4ZHa8gkm52HSzZy6vOPUFS4gq9VNfDKhQ5umZbIYzOyqKo4yP/P3p1Ht1WeiR//Xu263ndbXuMlsbOROLaTkMQSS5OQQgIDlJmWoYXOdDLdW5gOLZ1hKZ2W7qcFpkxLW0qZX6e0kLAGSCBOIIvt7Ktjx7Hjfd9lyZZ0f384Ngkk8Sb5SvL7Occnx86V9Pjq+tXzvvfe58n77//gofe20OOYfOJstcgMexT2eKk1pD+zWmTK2xz0Bnn1B7PuQvWHIGrNKxJRQRAEAVuyTIfDzYnZ0Boy2b9aQyaEhvOr9X/PoX95GGPiXP6tppF9fXbujI3kEUss7x/bTfZT3+Vn+7bjcE38lKyvWkP6o+IkGY8CHzTNjstLjnY66XQER9ItElFBEASBxaOtIWdB0uKvrSEzo+J44bbP8969D9ISlsSDtU1UOpx8Pj6a++PC+N+9rzPv6Yf5w5E9uD0TO91uS5Z5v9k3rSH9SbysY8Esqf6w5kL1h/eD5EY0kYgKgiAIaCSJNUnmWXGdaF6UgVg/bg25NDGNbZ/+Kv/vrq9Qpgnl4bpmulxuvpoUy2fD9fxw+/9xzW8e55UzR8Ytbm6zyPQPezjY7l9Jty9YZ1H1h8UqVH/wFZGICoIgCMDISmGtaA3pN67LmMf+ex/kJzffyxaHhh81tKKT4DvJ8azTD/HlLb9lzXM/4YO6qis+x1hryCBJWq7Gliwz6FYoa50Np+dD2NcyyKAK1R+8TSSigiAIAgDLL7SGnA1Ji9UiB0RrSEmSuD0vnxOb/5OvXncHz3Q5eLq5g0S9nu+lJbJguItbX/g5G//vaY63Nlz28VaLzM7GAb9Our1hrPrDLDl+hzzqVn/wFpGICoIgCMBIa8iVCWZKguTas6spiDMj66SAaQ2p02j5Qv4aKr/0PW4tXMsPmrv5Y1sXC2UTT6QnEdZ1nlXP/hefe+UP1HZ3XPJY24XWkKe7g3ule6QfewgljbOj+kNmuD4oJo0iERW84uWXX6agoIA1a9ZgtVo5ceKE2iFd0dGWet6pPsmQO7i7cAjCVNiSZY51BH9rSINWYnWif3Wpmcg4KusNPLhqPVVffpxl81fyUF0bWzp7KQ4P4cfpSXTXn2TRrx/h/nf+Soe9H7ioNeQsuP7XZpHpdLo5PhuqP1hkdjX6T/WHqRKJqDBtpaWl3HPPPbzwwgvs3r2bz3/+86xbt46+vj61Q7us9IgYPvXSb4n96QPc+bf/4bkje2kb8M9YBWGmrU6UkWZJa0irxX9aQ052HI02h/CjG27nxL8+SlzaQr5V28zO3n42RoXz/dQ4jp7eR85T3+X777+BwzV0oTVkYKz+Tsei0eoPsyDptlpC6B32cNjPqj9MlkhEhWl74okn2LBhA/PmzQPg7rvvxuVy8dxzz6kc2eVFmMx8c/kN9A05+Oupg3zu1edI+Pm3WPWHH/HDD7ZxvLUh6K+lEoQriTBqWRprCopTfuNZleQ/rSGnOo6mRkTz7C33sPefHmIwJp1v1TZxzO7g7rgovpMYxWvl28l5+j/oHaikqmcIV4Cvno1HI0kUJ5lnxfGbF2UgzqQN+N9Vp3YAQuDbsWMH3/3ud8e+12g0LFu2jO3bt/PlL3/Zq6815HJzqPn8tJ9nTWo2Bq1u7PS8gsKe+mr21Ffz7fe2MCcylptzFnFLziKs6XMxaMWfijB72CwyvzzWhX3Yg6wP3vWKUL2GggutIT+VHa5qLNMdR+fHWXj5zn9lb301D777Mm+cr+HOmAj+NTGGWucQ/3fob5w1bcI86MSjeNBIwfu+2iwhbK3pp6Z3iIxwg9rh+MzF1R++sTgaSZLUDmlKxKerMC0dHR309PSQmJh4yc8TExMpKyub0HPU19dffYOLTk019ndz42//a9JxTta57nZ+VfYevyp7jzCDiXVZ87k5exEbshcCwTuwCQKMnLL+6ZFO9rQMcmNKiNrh+JTVIvPjwx30DrkJN2hVicGb42gqBv503ad4r+EsPzjwLq93tXBXbCTfskTzq94ODg25cLk9GHTBm4gWXaj+sLPRzueCOBGFkeP3r9V9VPUMkxMZmL+raoloAn247V0M6vRqhQCA2z7sN7H4WzwTiaW3s5n05DhCTRoG+z68UzM+OpTIUMMlP7uS1Svyr/r/y/ShJMbn4NZo2L40iXTjTNdNc1NWfYyy6mN87x0tN8+34XLNxzHQzaBO/bmcY8CFx+3yi3j8LRaiElSNIVBZxlpDDgR/Ipok88ShDj5oGuSm9FBVYrDbR06tGo3GS35uNBrH/m88qampH/+hJMHibB6/oZB8SxxFIS0cRcvBh7/L4s//M3Jm1rRj90dGrYZrE0dOz38uN1LtcHyqIM5MiE7DzsaBgE1EpZm+Fk6SpBSgLjtnDi6nA43KS8mKAkMeBYNGQu1VbUVRcDqHQKvDoNMExr5RwOF0oNfr0Wo/XE0YHh7G4/F8bGC9HIdj/AutXWhobe8hPiEanTTzBXy10sj7odVoGFYkWoYNJOiH0EvqXm+lKAoDzmG6pBAS9MMYVF7k8Jd9M7pfWlvaAVIVRRln2T2wjI6jADk5Oeh8kPR3Od30DnlID1N/gj4ZLpeLyspKYOL7pnHAhU4jEW9WZ0XU7XZz5swZLBYLERERYz9vampicHCQzMzMcZ/j1KlTV/1/nclImlvLOc8Q8TExhBhAazSj1ZsC9pTu1fQPe2gbdJMWpkc7zq83lWPGn7QOuhn2KCSHeDfui/cLPhxHVdvbw595nOduXURRpkWtEACo7h3mW3tb+dHKeDLD1R1wW1pasN1xN9z2AH8IoH1TVFTE5s3/yn333Tv2s82bN6PT6XjyySfHfZ2Wlpar/n9bWxu3br4f3C18/89/Jj8l4qrbT0Sf08k/vf4nhj2Xv1s2JSyK69Lncl3GPAos6eg1H35AVfS4uO+DXn63Kpx5EeoOWC0tLay6/R6kTQ/xh9vncW2muiuA/rJvRvcLI4loUHv33XdJSUnx+vNWdDn5zI5Gnl6TSFGC2evP7yv19fVjq4MT3Te/O9XNHyq62X5LOobxshYfiYyM5Bvf+AYPPPDA2M8++clPotfr2bJly7iPH+8Sp6amJjo33MenXO1svOnf+XZCE85Ny1DcbqJTcolNXYBWF5grapfT43TzidfO8+DSGP4u8+rX/07lmPEnb9f18539bby2IZVE2Xvj7sX7xZdU+6SoHdSjGMIxh8WoFQIAWpeTFgbRylGYw8ZfvfMlXc8gtc3dEGD7JifvGnbvLedLXxsZQBVF4e133+ehhx6a0O+QMc42OlM9jS2doChkx6aQPyd9cr/IZXxv9+tUDX7YkUIjSaxMzuSWuYu5OWcR82OTrrhKYHI50WjtmEIi/eKYaWzphCEXWkOI6seMv+ybsf0iTNncSAOJ8kiXmkBKRKfClizz9IkuyloHWZUkqxLD9ddfT3l5+dj3iqJw8OBBHnrooQk9fiLJ0/9zdGFWhjhkycT9vy+T9a1v0dVbR0f9KbqaKolNXUC0ZR6aILg5M8KoJT/WxM5G+7iJaKC7NnGk+kNJo527VL7pbioC/2gTVPfggw9y4403cubMGebOncsLL7yAVqvls5/9rNqhXVaPY5Cf7d9BmMHE+qz53JyzmA3ZC4mV1bk+TBD8kSRJWC/Unvy3JYF7R+5EzAnTkxIyknSrlYjOxDj6lqMLs0bCqdVxKCkDS0kZ8X+3nijLXNrOH6P13GE6GyqIy1hMZEImUoDfWW+dbdUfGgZEIirMTkVFRTz33HN8+tOfxmw2o9FoeOuttwgLC1M7tMuq7engxb/7Z4rTc0RZJkG4CluyzP+d7aWie4jcKHVX/31ptDXkG+f7+Xa+osr1+TMxjp502cnQGknvbmNfei7Xb9uF/Hfr0RtlLDnLiUnOo7XmCI0V++ioO0X8nCWExaQE7CRkNlV/sFlkfqRy9YepEp/Cglfcdttt3HbbbWqHMSGLEwLr+h9BUMtYa8hGe1AnojCSdP+psofjnU4Wx5hUiWEmxtF+xcOKmtO8mVfAwMtPEe1wIplG3lujHE7q/DUM9s2n5dwh6k6UIIfHEj9nKSGRgVeBYrT6w86G4K/+UJwk88NDHbzfNMgGlao/TFXwrlULgiAI06LTSBdaQwZ255aJWDxLWkMOeNysOF9Br9HMibA4HB8c+Ng25rAYMhbfSPriG/B4PNQceYfzx9/D0d+lQsTTY0uWeb95MOg7SsXLOuZHGQOyy5JIRAVBEIQrsllkqnqGaOgfVjsUn9JIEmtmQWvIQTzkOPuIsfexN30ejm0lV9w2NCqJzPybSMlbjdPew9mDr9Nw+gOGHP0zGPH02Cwy/cMeDrYFdj/2ibBZZPY02xlyB1bSLRJRQRAE4YpWJJgxaKSgT9BgpDVkbf8wNb1DaofiU5pVS1l+/gx7M3Kxv70bxXPl2sySJBERn0F2wUaSsovo72qiquwVmqvKcQ35f3KXE2Eg6UL1h2BnS5YZdCuUtg6Ov7EfEYmoIAiCcEWyXkNRvGlWfJAvv9AaMuiTbmsRK2tO0xIaSbVLx9DBE+M+RNJoiLbMJbtwE3Fpi+hqrqKydAtttUdxu/x3tVwa7cfeOMBMN/CZaXPC9KSG6gLu+J3xRFRRlHpFUaRlBQUf66s726WkpHDq1CnEvrnU6H4xmcxiv3yEOGYub3S/KIoiBVtXJfhwHFUUZUaKb9uSQzjc4aDb6fb5a01XSkoKiqIwlX1j1GpYmWAOyqR7dL/k5eVhuX0DizsbkIed7EvPZfAqp+c/SqvTE5e+iJzltxKVlE3b+eNUlW2ls6ECj8c/jw+bRaZ10M3p7suvdE/nmPEno9UfShrteLyQdF+0X3w6jooVUUEQBOGqipNkFAV2NwVfgvZRVovMsU4n7YOX77oWDDQhMmGrllFQV8XejFwcb+2e9HPo9CYSswrILtxIaFQSTWfLOFv+Kj2tNX638jhW/SHIb0SDkeO30+nmeKdT7VAmTCSigiAIwlVFm7QsignMO3Ina02SjEaCXUGedJvXFbOy9jRVMYk0NXcxXFkzpecxmEJJzl1FVv4nMcoR1J96n+qDb9Df2eg3Can2QvWHkiB/TyEwqz+IRFQQBEEYl80is7dlEIfryje2BIMIo5alscF/Taxp7WoK6s+i83jYlz6PwW27pvd8oVGkLbyOOUvWotFoqT32LrVHdzDY1+GliKdntPpD/Syo/lCcFFiXl4hEVBAEQRiXzRKC062wP8DuyJ0Ka5JMWasD+3DwJt3auBiirpnL4qYa9qbn4nh7eonoKDkinowl60hbaMM1PEj1wTepO7kLp73XK88/VbOp+oPVEsL5AKr+IBJRQRAEYVxpYXrmhOlnxQe5LVlm2KOwpyW4k+7R0/PHktLpOFaFu6XdK88rSRJhMSlkLbsZy7wVDPa2c7b8VRrP7GfYqc7xI+s1LE8I/jqx8GH1h0BZFRWJqCAIgjAhtmSZXV66I9efXdwaMpiZ1hezvLYCt6ShPDWHwbcnf9PS1UiSRFRiNtlFm4ifs5Te9lqqSrfScu4QbtfMr9bZLHLAVH+YDqNWw7WJgXN6XiSigiAIAaqruWpGbwixJsl0D3k40h44d+ROldUS/K0h9ZlpJKbEMre9kX3p83C85Z3T8x+l0WiJTZ1PTtGtxKTk0Vl/msrSLbTXnZzRkk9rZln1h+MBUv1BJKKCIAgBqrFiH2cPvEZve92MJKTzo43EmrTsbAzulUKYPa0hzeuKWVFTQXlKNr17DuHp9917q9UZiJ+zhOyiTYTHptN67hBVpVsvTKh8fz1utEnL4hhjwKwUTsfqxMCp/uBXiajH46GoqIiMjAy1Q1Fdd08PjzzyCKtXr8Zms7FkyRIef/xxXC7/n934wjvbt+MccvKZu+/GarVy4sT4nUCC3V/+8hfWrl3L5+69l1OnTvHVr36V6upqtcPyK5IkfUWSJEWSJJvasfhCZv5N6Axm6k6UUHP4Lew9rT4dR0fuyJXZ2Wj3m9I8V9PZ2TnlcXRupIHEIGsN+fLLL3Pu3DnWrFkzNo6a149cJzqoN3AkNgXHe/t8HofeKGOZu5ysglswh8eOTKjKX5+RCZXVIrPvouoPo+PoDTfcQGFhIbfffntQjKPerP7g63FU54snnaqnnnqKyspKIiIi1A5FdbtKSnjxxRfZs2cPERERNDY2kp+fz9DQEI899pja4c2o0tJSHvz3f8eg1/PCn/5E6av/x7p16zh16hRhYWFqh6eau+++m9dee420Qit3b28gpGE769ev5+jRo5hMJrXDU11rayvAA2rH4UvmsBgyFt9If1cTLdWHOHf4bc7WtTHQ452bTi7Hlizz0rk+qnuHyYow+Ox1vOGNN96Y8jgqSRLWJJn3Ggf4tyXRSJI0Q1H7RmlpKffccw/Jycns3r2bP/7xj6xbt46TJ06QYVSw9HayL30exdtKkG+5YUZiMsrhpM4vZrCvg5bqQ9SdKEEOjyU+cykhEQk+eU2bJYRfHutif+sgVkvI2Di6du1aPB4P9913X9CMozaLzC+PdTEw7CFEP7V1x8bGRvDxOOo3K6INDQ08++yzfOELX1A7FL8QGRnF/fffP5aUWywW7rjjDv785z+rHNnMe+KJJyi2WpGkkcP17rvvxuVy8dxzz6kcmbo2bdrE2rVrR76RJD7zmc9QWVnJwYMH1Q3MTzz++OMAP1A7jpkQGpVEZv5NmOJzaW6o5Wf/+QU+ddNyhhz9Xn+tgjgzsi4w7siNiYmZ1jhqS756a8hA8sQTT7BhwwYMhpHJw+g4+sfnn0det4aVtRXsTc/FvmMvyvDMnnkzh8WQvvgG0hddj8fjpubwO5w//h6O/i6vv1ZamJ7McP1YwfeLx1GNRsOXv/zloBlHrZYL1R+ap/63+pWvfAV8PI76TSL61a9+lR/84AeYzWa1Q/ELxcVruO+++y75mclkYmgo8AfEydqxYweLFi4c+16j0bBs2TK2b9+uYlTqe/HFFy/53mA0AszKY+SjXn31VXQ6HcA2tWOZKZIk8a3v/oDURWs51+Zi7pxEqspeoflsOa5h713naNBKrEqUA+I60Ztuumla4+jSWBNhQdIacseOHRQWFo59f/E4al5vZUXtabrNIZw2ReDcO/NJmCRJhEZbyMzfQEreapz2Hs4efJ2G0x94fUJltcjsarLj9igfG0dHV0GDYRwdrf4w1ZJVr776Knq9Hnw8jvpFIjr6oXHTTTepHYpf27t3L3feeafaYcyojo4Oenp6iI2NveTniYmJQXEdjzcdPnwYi8XCqlWr1A5FVQMDAzz00EM8+O1vqx3KjBobRzdsoLnbxY9+8zpxaYvoaqqicv8W2mqP4XF7p6uMzSJzqmuIFnvgXbM+mXFUp5FYEwStIUfH0cTExEt+PjqOGlfmM3+gk0iH3StdlqZDkiQi4jPIKriFpOxC+ruavD6hsllC6BnycKTj48+3d+/eoBpHbckj1R+G3ZO79nZ0HP35z3/uo8g+pHoi2t/fz3e+8x1+8YtfqB2KX3v33Xc5f/483/3ud9UOZUbZ7SMfAKOnk0YZjcax/xNA8Xj43bPP8stf/nJ0Bjtr/cd//AebN28mPi5O7VBmzOXG0aFhF3Hpi8hZfitRSdm0nT9GZelWOhsrUDzTu0N5VZKMTiLgioNPZRwNhtaQo2Ol8cJZk1Gj46hkNCBfv5Ki8yOn5x1v7VL9ZjSNRku0ZR7ZhZs+MqE6its1vfciL8pAnEn7sctLnE4nP/7xj4NqHB2r/tA+uSR+dBxNSkryUWQf8lkiKknSIxfusrrs14Hyco4fPz6jv6w/eOSRR5Ak6YpfeXl52AcuPeXV0NDA5s2b2bp166y7kUuWZeDjp0mcTufY/wlQW1vLunXruP3229UORVWHDh1i//79bN68We1QvGK8cVSSJMrLy686jur0JhKzCsgu3EhoVBJNVWVUlb9CT2vNlJONUL2GZXFm1U7PjzeOju6Xi011HA2G1pCjY6XTeWn914vH0ZHT8xXUR8RQY3czfKxixuO8HK1OPzKhKhqdUB2nqmx6EyqNJFFskdnZcGn1h3/5l3/hjjvul5teeAAAIABJREFUCKpxNCfCQJKsm9TxO9PjqC/vmv8J8Osr/efia65pys1L4XvvvsuBAwfGrtOoqamhubkZm81GdnY2v/3tb30Y4sx74IEHrvrmVva5+frhDweLzs5ONm7cyNNPP01+fv5MhOhXYmJiiIiIoL390ruAm5ubyczMVCkq//LTn/4UKXIlX//619UORXWvvfYag4ODXH/99djDEgBG70r5hSRJ3cA/KYpSpV6Ek3bVcbSpqakpNjaWz3/+8+OOowZTKMm5q4hJmU9rzWHqT72Pqe4kCZlLCY2a/EKALVnmJ4c76BtyE2bQTvkXnIrxxlHgkst5pjOOynoNRfEmShrtfGZuYC4EjI6jzc3Nl/z84nHUdP1Kln7z+5hcw+xLz2X+thIMi3PVCPeydIaRCVV0ci5tNUdoqiqjo/4U8RlLCI9Ln3RVA5tF5m/VfZztHSY7wsCDDz6ITqfj+9//vo9+A3VIkoTVIvNuw8SrP1w8jl7g23FUURRVvpa9WK2c6nQoH/Xwww8r6enpH/u5r5zqdChXikUNF8fT29urXHvttcqWLVvG/v+ZZ55RJRY13XbbbcpNn/uiYkrOVk51OhSPx6MkJiYqv/rVr1SJx1/2i6Ioyg9/+EPlps99UVn2l7PKqU6HUl5erpSXl6sWjz/tm1OdDgXIABTApqg01vn467ImMo72dzcr1QffVI7vfF45d+Qdxd7bftXtP6plYFhZ9mK18mZt36QeN9O8MY6+dLZHKfxrtdLlcHk7vBlz2223KXfddZeSl5enKIpy2XG09e+/qvzL3T9V7vzCM0rz9Z9WK9QJGezrVGqPvasc3/m8UlX+mtLX0aB4PJ4JP97p8ihrXj6n/OZEp/LDH/5QueuuuxS3260oiqL6OOptpS12ZdmL1cqJjqmNy74eR1W/RlS4PKfTycaNG1mxYgXJycmUl5dTXl7OM888o3ZoM+7BBx+kZNeusc4bL7zwAlqtls9+9rMqR6auX//61zz//PP84z33YLfbOX78OK+++irHjh1TOzQhAIREJJCxZB2pC6y4hgapPvgmdSd34bT3Tujx8bKO+VFGvz5l7XA4vDKOFlsCvzXkgw8+yBtvvDF2mdPlxlHzujWsrD1NRXwKLTUtuGrq1Qp3XKbQKNIWXkfGkk+g0WipPfYutUd3MNjXMaHHG7QSqxNlflNyhOeff56vfe1rHDx4kPLy8qAbR5fGmgjXa/z3b9UX2e1Evj66atLU1KRYrVYlPT1dMRqNitVqVX7/+99PKXufDH9awVGUD+P57pO/UxiZgXzsa6Zj8Yd988u/vKZIcalK/oY7lOLiYuX48eOqxeIP+6W3t1fRaDQjx0TCHIV//8vIvzAjfzdX4g/7ZtQ//tvDCrDvwt/NYeDPivormD5dEZ3qOOrxeJTOpkqlYu/flBMlf1IaKvYpQ46BcR/37MkuZc3L5xSna+IrUTPpySef9No4eu+7Dco3P2j2QZQz56WXXlJMJpOyevXqy46jww0tyokMm3LNQ68p/3PdF5XeX7+gUqST4/F4lJ6280pl2SvK8Z3PK+dPlCiOgZ5xH/fy6VaFB19UCIv52PGh5jjqC/+xv1X51Ft1k37c1772NZ+Po5KiqHNnXMFfzyl/usFCbpRx/I196HSXk7t3NOIPsfhbPP4Wy9JFCzl07LhfxOIv+8Xf4vG3WHKjjIHdDmd8Xh3APW4XnY1naK87juJxE5OcR0zqfLS6y3dQOtszxF3vNPDL1QlcmxjcNw/+saKbZ052s+OWNEy6wD2ZOH/+fE6ePHnF/2/ZcB/3WwoxuIf5Yc8p4l/67xmMbnoURaG75SxtNUdxDQ0SmZhNXPoi9MbLH5v9wx5ufKWWb14Tw6eyw2c42pn1bv0A39rXypb1KaSETroigE/H0cD9axIEQRC8SqPVEZs6n5yiW4lOzqWj/hSVpVtorzuJx+P+2PaZ4XpSQnRBUfB9PDZLCE63wv7WQbVD8SnzujWsqD3NEcsceg6ewt3h/e5GviJJElGJ2WQXbiR+zlJ622upKt1Ky7lDuF0fL1AfqtdQEK9e9YeZ5M/VH0QiKkxbZWUl1157LTabTe1QBEHwAq3OQMKcpWQXbSI8Np3Wc4eoKt1KV3MVF59FkyQJmyWEkiY7HpXOrs2UtDA9c8L0Pku6/WUcHS3jNKzRUp6cieOdD1SNZyoumVCl5NJZf/qKEyqbReZAm4PeoY9PtIKJrNewPMHsl615RSIqTMvzzz/PPffcg0YjDiVBCDZ6o4xl7nKyCm7BHB5LY8U+zh54jd72urGE1GqR6XC4OdHpHOfZAt/FrSG9yZ/GUd3cOaTEhZLZ2cLe9FwG31Kvy9J0TWRCVZwk41bgg6bgXumGkeP3SIeDLqd/Jd3qH/VCQIuJiaGkpITs7Gy1QxEEwUeMcjip84vJzL8Jnd5M3YkSag6/hb2nlWtijUQa/PiOXC+yWeQrtoacDn8aRyVJwrS2mJU1pylLzWFgVxkeu3d/35l2tQlVnFk7Uv0hgCsiTFRx0oXqD372t+rLgvbCLLBhw4ZpP0d9/fglQpr7/GsGJwizkTkshvTFNzDQ1UTLuUOcO/w2YTHJXBubzc5GO19eFK12iD41P9pI7IXWkPlxZq8970yNoxNlXl/Mir8+wgv5Vo5GJRJfsh/zTVavPb9aRidUg30dtFQfou5ECXJ4LOtjcvh1jZYht4JBG7z3N0abtCyKMbKz0c7GOWFqhzNGtUQ0gT7c9i4Gder2c3Xbh/0mFn+LxzHgwuN24RjoZlB39UMlMtRIXFTohGu4XWz1ivE7nQzHpAHKhGLxtcnsl9kWj7/FQlSCqjEEI0mSCI22EBKVRG9bLa01h8nqOcDWjiwq20PJiY1UO0Sf0UgSxUkyJY12vrF4Yl1qZkpqauqEtsvLyxt3G0PBIrJxEt/fw770XFa9tSsoEtFRH51Q5fbsYYMSTnmdkWszgrvduM0i88zJbhwuj99Uf1Dtk+JeXRmOCj3VWnV3hMPt4V7dsF/E4m/x1DmNOO1zqDt5GL3x6td/faIwBefieKoPvjnp13nsm58ed5tGKZKHf/xH6k7uGjcWX5vMfplt8fhbLEtS7lQ1hmAmSRIR8RmExaYSWl/JL3f28+Kefdy3IJbYtIXo9Ca1Q/QJW7LMS+c+bA0ZjCStFvMnVrOipoI9GXkMvvU7FJcLyQ8m3t5y8YSqp7WGlNJ92E+9RYMjh7iMazCYQtUO0SdslhB+eayLfS2D2JJD1A4HUDER/b2rkB/NiyczXN1Vv+reYX6/t9UvYvGXeJ588imeeupJhmPSaN/0EJt/8QT6jvOXbPPii39l4cIFY9//5sXv0NDQwB//YfL9zkOSx18RPTsAmp/+aeQ6tQh1B8PhHhfGrl6/iMXf4vG3WATf02i0JKXlYs1s4niXma6mY3Q3nyUmZT4xKblotOqPq95UEGdG1knsbBi4aiL6yCOP8Oijj171ucrKyigoKPBKXHV1dRPabu3atRPazry+mBXffppXFhRxRisTW34M44ql0wnRL0mSRGTCHDpSwzhUV0FKZxM9bbVEW+YG5YRqtPpDSaNdJKIthKGVozCHqVv0Wuty0sKgX8TiL/H861e+yT/e+wUq+9x8uXyAJ/9xKzlh2ku2iY2NRXfR7Li730lbVz/msJhJv17GBB7j6HICEqaQSNXfJ5PLiUZr94tY/C0ef4tFmDnXp4TyaLOD6MW3oLSeou38MTobK4hLX0xUYjaSH9wR7g0GrcSqRJmSJjv/ND/qits98MADbN68+arPFRsb67W4UlJSvPZcAKY1hSzqaSHM6WBf2jyWbisJykR0lDUllH+qsvDZ7MUkDZ6jve4kXU1VxKYuCLoJlS1Z5qXqPtweBa1G/ctL1F/OEfxOaGgooaGhdBud6PVDxMXGkugHHYQEQfBfa5JkJAn2tLu5LbuA6JRc2mqO0FRVSkf9KeIzriE8Lt2vrqucKptF5qHSNlrsLhLky3+Mjo6jgUoymwixFlJYd4a9Gbl8btsrRDz8taB4/y5ncYyRKKOWkpZhvrJoMVFJc2mvO37RhGoRUYk5QTGhsllC+P3pHo50OLx6091UBf4eFQRBEFQXYdSyJMY0VjDbYAolOXcVWfmfxCiHU3/qfaoPvkl/V5PKkU7ftYlmtBJBX7LKvN7KytoKaqLiqe+y4zp9Vu2QfEYjSaxJMo81LNAZTCRmFZBduJHQqCSaqsqoKn+FntYa1GqN7i15UYax6g/+QCSiwrS88sor2Gw2tm3bxuHDh7HZbDz77LNqhyUIggpsFpmyVgf2Yc/Yz0yhUaQtvI6Maz6BRqOh9ugOao5un1KFDX8RZtBSEOe91pD+Oo6ablhFflMNBrebfem5DG4L3OL2E2GzhFDbP0xN74ftQC+dUEUExYRKI0lYLTI7G+x+kVSLU/PCtGzcuJGNGzeqHYYgCH7Alizzs6Od7G0Z5IaUS2+ECIlMIGPJOvo66mk9d5jqg28SHpdOfMY1GOVwlSKeOluyzE8Od9A35CbMoB3/AVfhr+OoNjqCyGV5LGk4y770eXxqWwnh37hP7bB8ZnmCCZN2pB97RvilN6KNTqgGelporT5E7dEdhEQlkjBn6ZTujVCbzSLzt+o+qnqGyYlUt/qDWBEVBEEQvMISoicnwnDFlUJJkgiPTSWr4JNY5q1gsLeNs+Wv0li5n2Gnf5wmnCjraGvI5uBuDWlab2XF+QpOJKTRfuY8roYWtUPyGaNWw8px+rGHRIxMqFIXWHE5B6k++CZ1J3fhtPfOYKTTt+xC9YcSL63qT4dIRAVBEASvsVlk3m8axHWVfuySpCEqMZvswo3Ez1lCb1stVWVbaT13GLdr6IqP8yfxso75UUa/uc7OV8zr1rC89gyKJFGaNhdHAPeenwhbsszxTiftg1cu//bxCVV7wE2oDFqJ1YmyXxy/IhEVBEEQvMZqkekb9nCwbfz+5BqtjtjUBeQU3Up0ci4d9aeoLN1CR/0pPB7/b+trtcjsabYz5Fb/Ojtf0aVaiM+0kNtaz970XAaDPBFdnThS/WHXBHrPXzqhWhpwEyqrReZ09xAtdnVrLotEVBAEQfCaeZEGEszaSd1RrtUZSJizlOyiTYTHptNSfZCq0q10N5/1i5sprsRmkbG7FMrbgvz0/LpiVtae5lBKFj2lR/F0B9Zp6MmIMGpZGmua1PE7MqGa/7EJVXvdSb+eUK1KktH5QfUHkYgKgiAIXiNJEjZLCDsbByadROqNMpa5y8kquAVzWAwNFXs5e+A1+jrq/TIhzQzXkxKiGyv5E6zM64tZWXMap1bHoYQMHO/uUTskn7JZZEo/Uv1hIj46oWo9d8ivJ1Sheg0F8d6r/jBVIhEVBEEQvMpqkWkZdFPRPbXTk0Y5nNQFVjKXrkenN3H++E5qjryNvafVy5FOj3ShDE5Jkx2PHyYa3qJfOJe0MANp3e3sy8hl8K3daofkU1aLzLBHYU/L1Fa6L5lQhcf69YTKapE50Oagd0i9lVuRiAqCIAhelR9nIkyvmfYpP3N4LOmLbyR90fV43C7OHX6b88d34hjo9lKk02ezhNDhcHOiM3hbykqShHndGlbUnmZ/2lwG3tuH4gje39cSomduhGHad5Qb5XBS5xf79YRqrPpDk3qXl4hEVBAEQfAqnUZiTZJ37siVJInQaAuZ+RtIyVuN097N2QOv0XB6D0OOfi9EOz3XxBqJNGj84u5jXzKtt7Ky9jS9RjMnQmNxfHBA7ZB8ypYss3uc6g8T5c8TKn+o/iASUUEQBMHrrBaZyp4hGgeGvfJ8kiQREZ9BVsEtJGUV0t/VSFXZKzSfPYBrWL3VOY0kUXyhS00wMy5fwtzhAaLt/exNnxf0ZZysSTL9E6z+MBH+PKGyWWT2tqhX/UEkooIgCILXrUwwY9BIXk/QNBot0cnzyC7cRFzaQrqaKqkq3ULb+WN43N5Jeifrcq0hg42k1xFyw0pWnK9gX3ou9rd3o3gmdzNPIJkbaSBR1nl9pfDKE6pyXMPeSXony5Y8Uv2hrFWd0/MiERUEQRC8TtZrKIw3+eyUn1anJy59MTlFm4hIyKSt9hiVpVvpbDwz4wlSUbwJ44XWkMHMtL6YFbUVNIdFUj2sZejQSbVD8hlJkrAmyVOq/jARH59QVVFVupW22pmfUM0JG6n+oNbxKxJRQRAEwSdsFpnDHQ66nb67I1dnMJOUXUh24UZCo5JoqiqlqvxVelprZuwOZZNupDVkyQSKoAcyk20FizsaMA8PsT99Ho5tJWqH5FO2ZJnWQTenp1j9YSI+nFDdSmRCFm3nZ35C9WHJNXWqP4hEVBAEQfCJYouMosD7M5CgGUyhJOeuIiv/kxjMYdSfep9zh96kv6vJ568NI0n3sY6rt4YMdJoQmfBV+RTWVY50WdoW3NeJLo01Ee6F6g8ToTOYSMwuUG1CZUuW6XS6Oa5C9QeRiAqCIAg+EWPSsShmZu/INYVGkb7oejKu+QSSpKH26A5qjm5nsK/Dp6+7OmnirSEDmXndyOn5ytgkmpq7GK6sUTskn9FpJFZ7qfrDRKk1oVocYyTKOLmOaN4iElFBEATBZ0buyB3E4ZrZ6zZDIhPIWLKO1AXFuJx2qg++Sd3J3TjtvmlPGWnUsiRmcq0hA5Fp7WoK66vQeTzsS58X9L3nbRaZqp4hGvpn9rrNmZ5QaSSJNUlmVao/iERUEARB8BmbJQSnW6G0debvCJYkifDYNLIKbsYydwWDvW2cLX+Vpsr9uIa8f4fwVFtDBhJtXAxRi3NY3FTD3vTcoC/jtOJC9Qe1JhgfTqisuJyDPp1QqVX9QSSigiAIgs+khenJCNOr2s9akjREJWWTXbiR+DlL6GmrpbJ0C63nDuN2ee9D15Y8vdaQgcK83sqK2tMcS0qn8/hZ3C3taofkM7JeQ5EPqz9MxMiEKpWsgk9imffhhKqxcj/DTu/FtTzBhEmF6g8iERUEQRB8ymaR2aXSHbkX02h1xKYuIKdwE9GWebTXn6SydCsd9afweKZ/Z78lRE+OF1pD+jvThetE3ZKGspQsBt95X+2QfMqWHOLz6g8TIUkaohI/nFD1ttVSVbbVaxMqo3ak+sNMJ90iERUEQRB8ymqR6R7ycKTdP/qTa/VGEjLzySm6lfDYVFqqD1JV9grdzWenfYey1SLzvpdaQ/orfVYaickxzG1vZF96btCXcSpOGqn+sNtPbkS7ZEKVnOvVCZXVInO8c2arP4hEVBAEQfCpBdFGYkxaVU/PX47eKGOZu4Ksgpsxh0bTULGXswdeo6+jfsoJqc0i0+fF1pD+yrzeyoqaCspTsundcwhPv3+9t94UbdLOePWHidDqjSTMWerVCdUaFao/iERUEARB8CnNhS41JY32GSsyPxlGOYLUBVbmLF2PTm/i/PGd1Bx5G3tP66Sfa16kgQSz1u+SFm8zrVvDytrTDOoNHI1NwfHePrVD8imbRWafCtUfJuLDCdUt055QRRi1LI2d2WtiRSIqCIIg+JwtWaZ+wEV1rzr94CdCDo8lffGNpC26Do/bxbnDb3P++E4cA90Tfg5JkrBaQijxUWtIf2FYMp8Mo0JSXxd70+cF/d3zo9Uf9qvUj30ijHI4qQusZE5zQmVNkimbweoPIhEVBEEQfK4gzoysk/x+pVCSJMKik8nM30BK3iqcA12cPfAaDRV7GHZM7PSzzSLTMuimwoetIdUmaTTIa9ewsuY0+9JzGdi+B2U4eLtKpYXpmROmV6XO5mSZL0yo0hddP6UJ1UxXfxCJqCAIguBzBq3EqkQ5YAq+S5JERPwcsgo3kphVQH9HA5VlW2k+ewDX8NVvusqPMxGm1/h90j1d5vXFrKw9TZc5hNOmCJx7D6odkk/ZkmV2NdlxB8CNaJIkERptmdKEyhKiZ26EgZ0NM3Pdr0hEBUEQhBlhtcic7HLSag+clTONRktMci7ZRbcSm7qQrqZKqkq30Hb+GB735S8zGGkNOfNlcGaa8dplzB/oJNJhnxVdlqxJMj1DHo50BM6NaBdPqJKyCunvbJzQhMpqkXm/eWaqP4hEVBAEQZgRqxLNaCUo8ZMyOJOh1emJz1hMTtEmIhIyaas9RmXpVjobz6B4Pn4tnc0SokpryJkkGQ3I162g6PwZ9qXPw7FtV1BfFzs/2kisSZ1+7NOl0WiJTp5HduEm4tLGn1DZLDL9M1T9QSSiwpR1dnbyyCOPsHr1amw2G0uWLOHxxx/H5Qqc1Q5BEGZOmEHLsjhTQFxndyU6g5mk7EKyCzcSGpVEU1UpVeWv0tNac0kStjLBjH4CrSEDfRwd7bJUFxFLrd3N8LEKtUPyGY0kUZwks9NPqz9MhFanJy59/AnV3EgDibJuRlb1dT5/BSFovfHGG7z44ovs2bOHiIgIGhsbyc/PZ2hoiMcee0zt8ARB8EM2Swg/PdJB35CbMINW7XCmzGAKJTl3FTEpebScO0z9qfcx158ifs4SQqOSLmkN+em5EVd8nkAfR003XMvS+/8Lk2uYfenzyNu2C8PiXLXD8hlbssxL5/o42ztMdoRB7XCmbHRCFZOSR1vNEZqqSumoP0V8xjWEx6WPVH9IknmvcYBvLY3xaSxiRVSYspiYGO6//34iIkYGWYvFwh133MGf//xnlSMTBMFfWS0ybgX2NPtvGZzJMIVGk77oejKu+QRIErVHd1B7dDuDfR3YLPK4rSEDfRzVhIcSXrSY/Pqz7E3PxfFWcHdZGq3+EIin5y9ndEKVlb8BgzmM+lPvc+7Qm/R3NWFLlmkd9H1bU7EiKkzZTTfd9LGfmUwmhoYmV7Kkvr5+3G2a+9Tt8SsIgnckyDryogzsbLSzLi1U7XC8JiQygTlL1tHXUUfrucNUH3yT7KgMPO5EdjfZuSUj7LKPm8lx1FfM64tZ8ft3+HnxJlq3NxNT24AuPVm1eHxptPrDzsYBPp8XqXY4XjM6oRrobqHl3CFqj+4gNjKRTH2Cz19btUQ0gT7c9i4GdXq1QgDAbR/2m1gAHAMuPG4XjoFuBnXqzhOmEsvZimPcd8/fM9jXMeHXWb0if9xthmPSACVg98tsicffYiHK94OoMHk2SwjPVXQz5FYwaCW1w/EaSZIIj00jLCaF7uaztNUeI82t8PqJfm6yzENnME/oefbu3cudd945qddOTU2d0HZ5eXmTet6JMK0tpujRp5AUhX1p88h4axdhX/gHr7+Ov7BZZB4qbaPF7iJBVv8zwJs+OqH6Z/0BYJFPX1O1PXivrgxHhZ5qrbpXBzjcHu7VDftFLAB1TiNO+xzqTh5Gb7x6rTp/i6Wvr5dPrb2GBQvyqD745oRf57FvfnrcbRqlSB7+8R+pO7kr4PbLbIrH32JZkjK5D3NhZtgsMv99oovytkGuTZTVDsfrJElDVFIOEfFzuEGp4NkzgxzftxVLai4xqQvQXmXR49133+X8+fO88cYbMxjx9Ogs8cTkZrCw+Tz70nPZtC24E9FVSTI6CUoa7XwqO1ztcLzu4glV44mTPn891RLR37sK+dG8eDLD1V2FrO4d5vd7W/0iFoDhHhfGrl5S5xeTGaHO2/Pkk0/x1FNPMhyTRvumh9j8iyfQd5y/ZJsXX/wrCxcuGPu+pbWVL97zWX72s5+SM3/+pF4vJHn8FdGzA6D56Z9U3S+j/OE98td4/C0WwT9lhutJDtGxs8EelIkowCOPPMKjjz4K0RY0//JLvvHuO9y94AOczmFe2V7Kjj1H2bt3HwUFBWOPaWhoYPPmzWzdunXsmtGJqqurm9B2a9eundTzTpR5fTHLXz/CHwpvoGfnS8R0dKONCZ5T1xcL1WtYFmdmZ+NAUCaioyRJQ8G8yX2eT4VqnxQthKGVozCHGdUKAQCty0kLg34RC4DJ5USjtWMKiVQtnn/9yjf5x3u/QGWfmy+XD/DkP24lJ+zSu1tjY2PRXTj12tnZye2fupsnnniCZcvXTPr1MsLGvyPP0eUEJFX3yyh/eI/8NR5/i0XwT5IkYbPIbKsb4EFFQSMFz+n5UQ888ACbN28G4J/29zM/Ip/1WRL9rZWsunYFGp0RS1I4iqIgSRKdnZ1s3LiRp59+mvz88SfnH5WSkuLtX2FSzOuKWfnU//Gb5Ws5YJmDZfv7hNx1s6ox+ZItWeYnhwO/+sN4ZL3vzxSrfy5a8DuhoaEkJiYSFxuLXq8nLjaWxMTES75Gk9C+vj5uueUW/vM//5Mbb7wRgP/5n/9RM3xBEAKAzRJCh8PNyc7gnDCMjqOJiYmsz4zmYK+GpJR05i37BLkrbyMy1kJzVSlnD7xGS92ZgB9HdfMySY4NJbOzhb0ZuQxuC/4uS24FPgiS6g9qEomoMGUOh4ONGzeyYsUKkpOTKS8vp7y8nGeeeUbt0ARB8HPXxBqJNAR/P3YYKVnVPeThSPtI0m2UI0hdYGXO0vUg6diz7Xm+cs86LPERATuOSpKEeV0xK2orKEvNYWBXGR574LTCnKx4Wcf8KOOsOH59TSSiwpQ9++yz7Ny5k5/97GcUFhaOfR08eFDt0ARB8HMaSaLYIs+KD/IF0UZiTFp2Ng5c8nM5PJa39p3l4Z89T9WZCk7t3cIL//0Ym25eF5DjqHl9MStrT9NvMHE0KhHnrlK1Q/Ipm0VmT7OdIXdgdlnyFyIRFabsS1/6EoqiXPZLEARhPFaLTE3fMLV9wduPHUaSbusVWkN+6Utf5uipGh76yZ/Y+Jmv8cUv3Ms7f/kl9af3MOwYuMIz+idDwSKyFQfx/T3sS89l8K0gPz1vkbG7FMrbxOn56RCJqCAIgqCK5fFmjFqJksbASrimwpYs0zDgorr38km3JElEJswhq3AjCVnL6O+op7JsK81nD+AaDozraCWtFvPaNaw4X8G+9HkMvr0bxRW81Ssyw/WkXKj+IEydSEQFQRAEVZh0GlYmmGfF6fn9UCI1AAAc80lEQVTR1pDj/a4ajZaY5Fyyi24lNnUhXU2VVJVuoe38MTxu/185Nq9bw4qaCtpCwqnUmBkqP6Z2SD4zUv0hhJImOx5xJnDKRCIqCIIgqMZqkTnW4aTDEbwrZzDSGvLaC60hJ0Kr0xOfsZicok1EJGTSVnuMytJX6GysRPF4fBzt1JmKi1jU00LokIO9s+T0fIfDzYkgrf4wE0QiKgiCIKhmTZKMJMGuWbAqarPInOoaosU+8aRbZzCTlF1IdsEthEQl0lS1n6ryV+lpq/XL6/Els4mQ4kKKzp8ZOT2/bZdfxukts6n6g6+IRFQQBEFQTaRRy5IYEyWz4IN8VaIZ7YXWkJNlMIeRkruKrPwNGMxh1J/czblD2+jvavJBpNMzcvd8BeeiE6jvHMB1+qzaIfnMaPWH2XD8+opIRAVBEARV2Swypa0O7MP+e8rZG8IMWpbFTS/pNoVGk77oejKu+QQAtUd3UHt0O4N9Hd4Kc9pMN64mv/EcBrd7Vtw9b7OEUNM3TE3vkNqhBCSRiAqCIAiqslpkhjwKe1uCvwyOzRJCedsgfUPuaT1PSGQCc5auJ3V+McNOO9UH36T+1G6GBvu8FOnUaaMjiFiWx5LG6rHT88FseYIJk1YSq6JTJBJRQRAEQVXJoXqyIwyz4oPcavFea0hJkgiPSyOr4GYsc5dj72mlquwVmipLcQ2pm9Sb11tZXlvBiYQ02itqcTW0qBqPLxm1GlYkmClpCv7j1xdEIioIgiCozmaR2d1kx+UJ3htbABJkHXlR3k26JUlDVFIO2YWbiM9YQk9rDZWlW2k9dxi3S52ST+Z1xaw4X4EiSZSlzcXx9m5V4pgptgvVH9oHg7v6gy+IRFQQBEFQnc0i0zfs4WBb8PYnH2WzhPCBD1pDarQ6YtMWkFO0iWjLXNrrT1JVuoWO+lN4PNO7FGCydGkW4uckkdtaP1LGaVvJjL7+TBur/iBWRSdNJKKCIAiC6uZFGkgwa2fN6XlftobU6o0kZOaTU3QrYbGptFQfpKrsFbpbqn3yeldiWmdlZe1pDqZk0VN6FE+P+tev+krELKr+4G0iERUEQRBUJ0kSVksIOxsHgrruJEBWuJ7kGWgNqTfKWOauIGvZzZhDo2k4vYchRz99HfUzso/N69awsuY0Tq2OwwnpOHbs8flrqmm2VH/wNpGICoIgCH7BZpFpGXRzpju4y+CMtIaUZ6w1pDEkgtQFVuYsXYckSZw/vpOaI+9g72nz6evqF80jLVRPWnf77CjjlCwzPEuqP3iTSEQFQRAEv5AfZyJMPzu61Iy2hjw5g60h5fA49MYQ0hZdh8c9xLnDb3H++E4cA90+eT1JkjCvL2ZFbQX70+Zif3cfinNkkjF89jyD7wbXCqklRE9OhGHCbVyFESIRFQRBEPyCTiOxOsk8KxLRa2JMqrWGDItOJjP/kyTnXotzoIvqA6/TULGXYYf3EyjTumJW1J6mxyRzIiwGxwflDJ8+S9vfbcYdhCWdbBaZ95sGg776gzeJRFQQBEHwG1ZLCJU9QzQOqFN2aKZoNSOtIdVKuiVJIjIhk6zCjSRkLaO/o57Ksq00Vx/EPey9VVrjiqXMG+oj2t7P3vRc+n/9v7Td/kU8bZ3gntk7+WeCdRZVf/AWkYgKgiAIfuPaBDN6jeTzG3n8gdUiU9M3TG2fekm3RqMlJjmX7KJbiU1dSFfjGSpLt9B2/jge99RqYnp6+2n/7AN0feuH9D/3NwyZKSw/X8G+9Hk43i/H09VzYcPgWzUcrf4wG1b1vUUkooIgCILfkPUaiuJNs+KDfHm8GaNWosQPrinU6vTEZywmp2gTEfFzaKs9SmXpVjobK1E8k7sLXBMeivmWGxj40xZ6/vPnDB86ycraCprCoqiNihvbbrLPGwhGbkQLoWQWVH/wFpGICoIgCH7FapE53OGgxxl8p24vZtJpWJngX9fE6gxmknKKyC64hZDIBJoq91NV/iq9bbWTSqzk29djWlc89v3ixnOYh4fYl5774UZBeGoeRo7flkE3FUFe/cFbRCIqCIIg+BWrRUZRYPcs6FJjvdAassPhX60hDeYwUvJWk7VsAwZzGHUnd3Pu0Db6u5on9HhJkoh64t/RRIWPPJ/HTWF9FfvS5324URCemofZVf3BG0QiKgiCIPiVGJOORTHGWfFBPtYa0k9/V1NoNOmLrifjmhsBqD26ndqjOxjs7xz3sdr4GCK//29j36+oOc2ZWAttISPJqRKkK6I6jcSaJPVuRAs0IhEVBEEQ/I41SWZvyyAOV/BdR3ixyABpDRkSmcicpetJnV/MkKOf6gNvUH/qfYYGr96207zpRsw3Xw9AQX0VWsXz4apoEF9DabXIVPUM0dAf3NUfvEEkooIgCILfsSWH4HQrlLYGfxmcQGkNKUkS4XFpZBfegmXucuw9LVSVvUJTZSmuoct3E5Ikicgf/BuamChChxwsbqxhX9qFRDRIV0QBViaYMWgkv59g+AORiAqCIAh+Jz1MT0aYflZ0qbFaZIYCqDWkJGmISsohu3AT8RlL6GmtobJ0K601R3C7Pr4CqI2JIvKHI6foV9ae5qglg36DKWivEYXZVf1hukQiKgiCIPglq0VmV+PM9GNXU3KonuwIQ8Ctnmm0OmLTFpBTtIloy1za605QVbqFjvpTeDyXrnbKn7we861rWVFbgVvSUJ6SjeL27xXg6Rqt/tAd5NUfpkskosKUOZ1OHn74YaxWKzfeeCNLly7ltttuo7q6Wu3QBEEIAjaLTPeQhyPtM9ePfaaNjqMH/t9/86s397Akf1nAjaNavZGEzHxyim4lLCaFluqDnC17he6W6ktKPkU+fj/xoQbmtjeyLyMXlOBORItnUfWH6RCJqDBlXV1d/OY3v+Evf/kL27dv58CBA+j1eu666y61QxMEIQgsiDYSY9IG3ErhZIyOo7//zhfJWrCYX7+xK2DHUb1RxjJvJVnLbsYYGkXD6T1UH3idvo56FEVBGx1B1I8eZEVtBWUp2Qy5g3ule7T6QzAfv94gElFhyqKjo3n99ddJSEgAQKPRsGbNGs6cOaNyZIIwO5xXsTXkTNBIEtYkmZ1B3KVmdBxdlZVEglnL7iZHwI+jxpAI0hbYmLNkHVq9gfPHd1Jz5B3sPW2Y167hugWJDOoNHNKEqB2qz9kss6P6w3SIRFSYMoPBwNKlS8e+b2ho4LnnnuNrX/uailEJwuwxG27ksSXL1A+4qO4NzqR7dByVJAmrJYRt1Z38IUjGUTkijvTFnyBt4XV4XEOcO/wW50/sJO+bd2EZGmC3NlLtEH3OZhmp/rC/NTBuRFODTu0AhMDX0NDAxo0bOXHiBPfffz+PPfbYpB5fX18/7jbNfeJib0H4qPfq+7hnXnB/mBfEmZF1I2VwsiIMaofjMw0NDfzu21/nTP7f84VP3sljj/77pB4/kXFUDZIkERaTTGi0hZ7Wc7TWHKGmo4T7Vph4oT4Ej6KgkSS1w/SZtAvVH0oa7Vgtwb8CPBWqJaIJ9OG2dzGo06sVAgCOARcetwvHQDeDOvXzcn+KZ6KxRIebeH/n27S2tvGlL32RB77xJb43iWR09Yr8cbcZjkkDlIDaL7MxHn+LhagEVWPwtfK6Viqresiak4tGq/6x6AsGrcS1iSNdau7LC96kOzk5meNv/IXiv1Wybet+/vmf/5nf/OY3E358amrqhLbLy8ubaojTIkkSkQmZhMel09V4BrtylH9QznHkeAiLc5eg1RtViWsm2CwyL5/rw+1R0GqCN+meKtVGrnt1ZTgq9FRr1b06oM5pxGmfQ93Jw+iN6t+Z6Q/xNDY20tTUSKMUSZfhera9+AJHle5LtsnLy0OWPz67e+jLd1B55gwn97yEyWSe0Os99s1Pjx+TFMnDP/4jdSd3qf4++cN75K/x+FssS1LuVDUGX9PpjWyrqGVdewWxaYuJSspCkoLviiubRea7pW202l3Ey4GRcD/yyCM8+uijV92mrKyMgoKCse91Gokb0iN5f91d/PaeAr7+9a+zYMECX4c6ozQaLTEpeYQnZPHSmx8Q11hJZW8NsakLiE4OzgmVzSLzh4oejnQ4yI+b2OfibKLaO/57VyE/mhdPZri6K6LDPS6MXb2kzi8mM0L9PwB/iCcx147dbqeqX+F/jyosX/z3ZIdeOouLiopCunA6RaP58IOvubmZf9j8CL/4xS9Yd+26Cb1eSPL4K6JnB0Dz0z/5xfvkD++Rv8bjb7EEu8LkGM4QwW0RtTRV7qej/iQJc5YQFps29vcZDFYlmtFKUNJk586scLXDmZAHHniAzZs3X3Wb2NhY3Be6C2m1WmDkmsKtVaEQEcfJkycnnIjW1dVNaLu1a9dOaDtf0+sNmCwL+X17Gj+O76C19iidjcE5oZofbST2QvUHkYh+nGqfFC2EoZWjMIepuxxvcjnRaO2YQiJVj8Vf4jGHxRADDHQ5MVQ0kpRiITXq47H84Q9/oL29nQceeGDsZ22nzlLb0EZcUjrmsJgJvV7GBLZzdDkByS/eJ394j/w1Hn+LJdjZLDJPHu8ietW1xKTOp/XcIepO7sYcFkNC5lJCIhPVDtErwgxalsWZ2NkQOIloaGgooaGh42730XF0ZYIZxTUMOUVYLJYJv15KSsqUY1WLzRLCKzX9DCUuJTslj9aaIxdNqJYSFpsaFBMqjSRRnDRyecnXF0cHxe/kTcEz5RBU8bvf/Y729nYAHA4H3/ve91i4cCGFhYUqRyYIwW+0NeS+lkHModGkL7qBjGtuBKDmyHZqj+1gsL9T5Si9w2YJobxtkL6h4Ltx8eJxVOMeov/4XqKWrwv6cbQo3oRRK1HSOIDBHEZK3moyl23AYA6l7uQuzh3axkB3s9pheoUtWaYhiKs/TIdIRIUpu+GGG/5/e/fy1NaZpgH8+Y7uR9wFAh1xkTFKTHzBwQHHxLZOyp3ErrRjr7q6qjepmqkss+2qbHpmlZrF9GIy2Y3/gdlM7LhdnaRn2rfYMdgQO75zs7lagABzFRdJsxAQ2sZGAsHROef5bS3QJ6COn/c753tfHDt2DB9++CGOHj2KpqYmFBQU4MKFC7DbjXu6lShbLI+GXD3P2l1Qhh1vH0fFW0cxPzuFrlsX0PfgKuZnJzVc6eaFFBmxBHDtmbHa4Kx1Ha2cC6Oy6UPMJixaL29LOa0SDpW6/uHv16gF1XL3B86ef5n2D7iRblVUVOCrr77SehlEpqYqMv67YwKL8QSsSydyhRDIK6lEbnE5xgY7Mfz0DjpazqHQF0RJ1V5Y7fp7Tq1UtqK2MBm6P6pc/5a3Xqx1HY1EF3H8fC+uDM7gt4FcjVa2PVRFxr/eHEEkugiP89dIslxQTY70Itzdhq5bF5DvDcAbqIPdpb+fid0i8F5ZcjjDPxm4+8NGcEeUiEjHQoqMiYU42kaiL/2bEBKKlCCCjafgDdTh+VA32pvPYujJbcQW9XeLMOST8eOzGY6GNJDDPhlCAJfX+KzLBVVNw0n4ggcxPR5GR8s5DLY3Y3FefzvjIUXGg7F5hGeMf5AyHQyiREQ6tqvADq/r9fPYJYsVxZV7EGw8jULlDYz03kNH8zeI9D1APK6fZy5VvxsziwncHNZfCElXyCfjmglGQxY4LNjvcb7279coBdVK9wcTFBjpYBAlItIxIQRUxY2LAzPrzmO32Bwoq65HsOEUcjzlCHe1orPlHMbDXbqY5b4zzwa/24qL/cb/j1z1J0dDNg+9vNNtNKoio3koipmF14duvRdUuXYL3ilxmWI0bzoYRImIdE5VZDybWcTj8fmUXm9zuuF/8xCqD3wMR04h+h9eQ1frXzAZ6c/qQJqcxy7j8uAM4lm8zkyoWhoNaYbQovqT3R+uh1Pb6dZzQRVSZNwajhqy+8NGMYgSEelcfYkTOTYJlwbT2yl0ugtQuVvFjv0fQbLY0XP373h65wfMTAxv0Uo3T1VkjERjuD9q/D6xIUXG5QHjh27FbUMw3572LWs9FlTL3R9+NFj3h81gECUi0jmrJHC4zLXhW9ZyfgkCdR+gco+K2MI8utu+Q++9S5ibfp7hlW5enceJfLtkijY4qiJjfD6O2yPmCN1XBmewGE8/QK4uqCzW7C6oVnd/oCQGUSIiA1D9bjx+Po+B6Y0d3hBCINdTjuoDH8O/qwmzU6PovHUeA4+uY2Eue/7TtEjJKTVmOPCxu8gBj/P1B9GMQlVkTC7E0Tq88Wdi5fwSVO37AJV73l8pqHruXcy6gkpV3Lhmgu4PqWIQJSIygKZSF2yS2HRoEUKgoLQaNQ2foLS6HpORPrQ3f4NwVytiC9mxM6f6ZXRPLqBnUj8npjdCEgIhX7L3ZLbeas6UNwvsKF2n+0MqkgWVf6Wgik6NZV1BpSqyabo/pIJBlIjIAGSbhAavM2O3/CTJAk95LWoaT6O4YjdGBx6jvfksRnruIh7Ttg/iQa8LDoswzUGevulFdBs8dCcPorkzFrqzuaCqNlH3h1QwiBIRGYSqyGgbieL5XOZO5FqsNngDdQg2nkK+N4ChJ7fR0XIWY4PtSCS06XHptEp494XRkEa1MhrSBKFFVWSEZ2N4lGL3h1RkY0GVbLkm45IJuj+kgkGUiMggjvpkxBPA1WeZDy1Wuwu+YCN2NpyEnO/FwOMb6Lx5HhPDPZrcNlYVGb9E5jAaNXYbHLtFoKlMNkXori9xItcmbckzsa8qqEYHtCmoVMWNSDSGeybo/rAeBlEiIoModlmxt8ixpbtnDlceymuPoLr+BGwON3rvX0Z3218xPf5sy95zLUeWR0Om2bJKj1RFxv2xOQwZfDSkVRI47Nvane7lgqqm4RPI+aUYbNemoKordqDAvjWhW28YRImIDERVZFwPz2IutrW7PK5cD6r2HUPVvt8AAJ7c/hue/vK/iE6Nbun7LlseDXmx3/jPia6MhjRF6HajfRPdH1Jld+WivPawZgWVJASOKubY6V4PgygRkYGEFBnRWAI3wtszGjKnsAw73j6OireOYH52Cp23LqDvwVXMz05u+XunOhpS73LtFhwocZriOdFDS90ftuuzallQqYobTyYX8NTgB9HWwyBKRGQggTw7qnK2dzSkEAJ5JVWoeeckfMGDmB4Po+Pmtxhsb8bi/Na1qAkpydGQP6U4GlLPVMWNm8Ozhh8NKdskNGaw+0OqtCioGr1OOCwCl0zQ/eF1GESJiAxG9cu4Mji77SdyhSShSAki2HgKJVX78HyoG+3NZzH05A5ii5nf9fHn2FCTb44pNcujIa+ZYDSkqsj4OZLZ7g+p2O6CymmVcMgk3R9eh0GUiMhgQoqMsbkY7kS0OZErWawoqdyDmsbTKFTewEjvXXQ0f4NI/0PE45kNFyHfxkdD6snyaEgzHG45qshIJIArGj0T++qC6nbGC6rQUveHSNTYB9Feh0GUiMhg9hQ5UOSwaP5ModXmQFl1PYINp5DjKUe48xY6W85hPNyVsRPKqj85GrJtZHueidWSqrhx1QSjIT1OK/Z6HJrvFL5cUN3LeEG10v3BBAXGqzCIEhEZjCQEQkr2jIa0Od3wv3kI1Qc+hsNdiP6H19DV+hdMjvZven27CuzwurQP3dshZKLRkCFfsvtDdFH7g2hbWVCtdH9gECUiIiNRlewbDel0F6Byj4od+z+CZLGj55e/4+mdHzAzMbzh75mcUpO50ZDZbOfSaEgz3J5X/W7MxRJoHsqene5XFlSRzRVUZun+8CoMokREBtTgzd7RkHJ+CQJ1H6Byj4rFhTl0t32H3nuXMDfzfEPfb3k05OMMjobMRmJpp/vSgPFHQ1bl2hDI3d7uD6l6qaC6u7mCKqTIWIgncN0E3R/WwiBKRGRAdovAodLsbZgthECupxw7D/wW/l1NmJ0aRefN8xh4dB0Lc+mtub7EiRyblLWfNZNURcZINIb7JhgNGVJkXM7i0L26oIotzG+4oPLn2BDMt2dl6N4ODKJERAalh9GQQggUlFajpuETlFbXYyLSh/bmbxDuakVsIbWwZZUEDpe5THHLus7jTI6GNMWUJRnj83HcHsne0L1cUFUf+HhTBVVIkXF1cNbw3R/WwiBKRGRQ7/n0MxpSkizwlNci2HgKxeVvYXTgEdqbz2Kk5x7isfWDtOp34/E2jIbUmkUSOOKTs/KRi0zbXeSAx2nRxU7hZgsqVUl2f2gdzp5nYrcLgygRkUHlLY2G1NNOocVqh3fHfgQbTyPfG8DQk5/R0XIWY4PtSCRefZijaZtHQ2pJ9cvonlxATxYdRNsKkhAI+ZLPxOrlINqvBdVpFFfsxujA45QKqjcL7Ch1WUzxeMmLGESJiAxMVdxoGdLfaEir3QVfsBE7G05Czvdi4PENdN48j4nhnjVDiWyT0OB16mL3d7MOel1wWIQudgo3S/Unuz90TegrdFusNngDdQg2nkqpoEoeRHPjkgm6P7yIQZQyIh6Po7GxEYFAQOulENEqR3U+GtLhykN57RFU15+AzeFG7/3L6P75O0yPh196rarIaBvZ/tGQmZLqddRplfCuSUZDvlOy1P1Bp581nYJqufvDI4N3f3gRgyhlxNdff4329natl0FELyiTrdhVoP/RkK5cD6r2HUPVvmNAIoEnt3/A01/+D9Gp0ZXXHPXJiGs4GnKz0rmOqkujIUej+gzdqbJbBJrKZN3//aZSUNWXOJFrku4PqzGI0qb19/fjzJkz+Oyzz7ReChGtQVVkw4yGzCn0Ycfbx1H+1hHMz06is/UC+h7+iPnoFIpdVuwtcugytKR7HV0ZDanT0J2O5e4P4Szu/pCqXwuq37xUUFklgcM+c3R/WI1BlDbt888/x5dffgmXy6X1UohoDSHFbajRkEII5JdUoeadk/DVHMT02DN0tJzDYEcLjpTacC1LRkOmI93r6MpoyH7jPyf6XtlS9wcDBbScwrJ/LKhuXUDfg6t4vziB9ufz6J/S1zOxm2HVegGkb99++y2sVitOnDiBGzdubOh79PX1rfuaZ5PGvv1EtJVq8m1Q5ORoyKYyWevlZIyQJBQpQRSUBhDpf4hI731UzvVgemYXrg9O4f2KPK2XmJKNXkdVRcZ/3h3DzEIco+GBLVyhtnJXdX/4XY0+fqepWC6o8jwVGHvWieGnd+Cdf4rjlmJc6ZXx+9pSrZe4LTQLovHYIqLT45i1apuFo9OLWbOWbFvPemuZmZnBf/z533DmzH9hdjICt0OC4i3E7GQkrfc5/G79uq9Z8FQCSOji52Lm9WTbWlBojgv5eoQQUP0yvu+dxh/fTkASQuslZZRksaGkci8KfW+goOcuSgYn8D8trdgnlaHQF4QkWbRe4itNTU3hiy++wPfff5/214YUGX++M4qfwrM4VlGR0tfU1tam/T7ZQFXc+PfbEUzOx5Brz97f50b8WlDtQKT/Id6dbkO86zsMufbDU14Li9Wm9RK3lDBbmwBanxDiXwD8aZ2XNQD4A4CORCLx9aqv+zSRSATSfL9U/wivJRKJ99L53kREWuB1lCg1DKL0EiFEDoCcdV42AuAWgOcAlh/GCgAoA/ATkhfWf07x/cpTeV0ikVj/Hj4RURbgdZQoNQyilDEbreSJiCiJ11EyG56aJyIiIiJNMIjSpgkhyoQQFwF8CqBMCHFRCPGpposiItIRXkfJrHhrnoiIiIg0wR1RIiIiItIEgygRERERaYJBlIiIiIg0wSBKRERERJpgECUiIiIiTTCIEhEREZEmGESJiIiISBMMokRERESkCQZRIiIiItIEgygRERERaYJBlIiIiIg0wSBKRERERJpgECUiIiIiTTCIEhEREZEmGESJiIiISBMMokRERESkCQZRIiIiItIEgygRERERaYJBlIiIiIg0wSBKRERERJpgECUiIiIiTTCIEhEREZEm/h8Fi0sGSz43VwAAAABJRU5ErkJggg==\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_linear_transformation(A)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Key idea:\n", "\n", "> A **linear transformation** keeps the origin in place and transforms straight lines to straight lines.\n", "\n", "The third episode of the series [_\"Essence of Linear Algebra\"_](http://3b1b.co/eola) uses wonderful animations to illustrate the idea of matrices as linear transformations [3]." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's practice with another example. Consider the matrix:\n", "\n", "$$ M = \\begin{bmatrix} 1 & 2 \\\\\n", " 2 & 1 \\end{bmatrix} $$\n", "\n", "The first column corresponds to the vector where $\\mathbf{i}$ lands after the transformation, and the second column is where $\\mathbf{j}$ lands:\n", "$$\n", "\\mathbf{i} = \\begin{bmatrix} 1 \\\\ 0 \\end{bmatrix} \\Rightarrow \\begin{bmatrix} 1 \\\\ 2 \\end{bmatrix} \\\\\n", "\\mathbf{j} = \\begin{bmatrix} 0 \\\\ 1 \\end{bmatrix} \\Rightarrow \\begin{bmatrix} 2 \\\\ 1 \\end{bmatrix}\n", "$$\n", "\n", "Any arbitrary vector on the plane, $\\mathbf{x} = \\left[ \\begin{array}{c} x \\\\ y \\end{array} \\right]$, is transformed to: \n", "\n", "$$\n", " x \\left[ \\begin{array}{c} 1 \\\\ 2 \\end{array} \\right] + \n", " y \\left[ \\begin{array}{c} 2 \\\\ 1 \\end{array} \\right]\n", "$$" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[1 2]\n", " [2 1]]\n" ] } ], "source": [ "M = [[1,2], [2,1]]\n", "M = numpy.array(M)\n", "print(M)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([1, 2])" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M.dot(i)" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([2, 1])" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M.dot(j)" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_linear_transformation(M)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To see what the transformation does to one particular vector, we can use our custom function `plot_vector` again, using the vector and its transformed self. Try several different ones…" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x = numpy.array((0.5,1))\n", "\n", "vectors = [x, M.dot(x)]\n", "plot_vector(vectors)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Note:\n", "\n", "When we represent a matrix in Python using the NumPy array data type, we define it by listing the **rows** of the matrix. We didn't emphasize this in the examples above, where we chose matrices whose rows matched the columns! But that's just a coincidence. Look at another case:" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 1 2]\n", " [-3 2]]\n" ] } ], "source": [ "N = numpy.array([[1,2],[-3,2]])\n", "print(N)" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_linear_transformation(N)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Exercise:\n", "\n", "Create a $2\\times2$ matrix of your choosing (as a NumPy array of the row list), print it, then multiply it by the basis vectors $\\mathbf{i}$ and $\\mathbf{j}$, and finally visualize it using our helper function `plot_linear_transformation()`." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Matrix-vector multiplication\n", "\n", "Consider again the matrix $A$ defined above. As a linear transformation, it transforms any arbitrary vector on the plane, $\\mathbf{x} = \\left[ \\begin{array}{c} x \\\\ y \\end{array} \\right]$ , to: \n", "$$\n", " x \\left[ \\begin{array}{c} -2 \\\\ 1 \\end{array} \\right] + \n", " y \\left[ \\begin{array}{c} 1 \\\\ -3 \\end{array} \\right]\n", "$$\n", "\n", "Since applying the linear transformation *is* computing the matrix-vector multiplication $A\\mathbf{x}$, we see that matrix-vector multiplication is a combination of the matrix columns scaled by the vector components:\n", "\n", "$$\n", " A\\mathbf{x} = x\\,\\mathbf{a} + y\\,\\mathbf{b}\n", "$$\n", "where the vectors $\\mathbf{a}$ and $\\mathbf{b}$ are the columns of $A$.\n", "\n", "##### Key idea:\n", "\n", "> The matrix-vector multiplication $A\\mathbf{x}$ is a linear combination of the columns of $A$ scaled by the components of $\\mathbf{x}$.\n", "\n", "This is also the case in 3 dimensions. Consider the matrix $B$ and the vector $\\mathbf{y}=\\left[ \\begin{array}{c} x \\\\ y \\\\z \\end{array} \\right]$\n", "\n", "$$ B = \\begin{bmatrix} 1 & 2 & 4\\\\\n", " 2 & 1 & -1\\\\\n", " 0 & 3 & 1 \\end{bmatrix} $$\n", "\n", "$$ B\\mathbf{y} = x\\left[ \\begin{array}{c} 1 \\\\ 2 \\\\0 \\end{array} \\right] + \n", " y\\left[ \\begin{array}{c} 2 \\\\ 1 \\\\3 \\end{array} \\right] + \n", " z\\left[ \\begin{array}{c} 4 \\\\ -1 \\\\1 \\end{array} \\right] \n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Some special transformations\n", "\n", "### Rotation\n", "\n", "Imagine that you want a transformation that takes any vector and rotates it 90 degrees to the left. You can visualize that the unit vectors need to be transformed as follows:\n", "\n", "$$\n", "\\mathbf{i} = \\begin{bmatrix} 1 \\\\ 0 \\end{bmatrix} \\Rightarrow \\begin{bmatrix} 0 \\\\ 1 \\end{bmatrix} \\\\\n", "\\mathbf{j} = \\begin{bmatrix} 0 \\\\ 1 \\end{bmatrix} \\Rightarrow \\begin{bmatrix} -1 \\\\ 0 \\end{bmatrix}\n", "$$\n", "\n", "That means that the matrix that transforms all vectors by a left 90-degree **rotation** is:\n", "\n", "$$ R = \\begin{bmatrix} 0 & -1 \\\\\n", " 1 & 0 \\end{bmatrix} $$\n", "\n", "The rotation of any vector $\\mathbf{x}$ is the multiplication $R\\mathbf{x}$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Shear\n", "\n", "Another special transformation turns every square into a diamond shape by leaving $\\mathbf{x}$ unchanged, and transforming $\\,\\mathbf{j}$ so its tip falls on the coordinates $(1,1)$: \n", "\n", "$$\n", "\\mathbf{i} = \\begin{bmatrix} 1 \\\\ 0 \\end{bmatrix} \\Rightarrow \\begin{bmatrix} 1 \\\\ 0 \\end{bmatrix} \\\\\n", "\\mathbf{j} = \\begin{bmatrix} 0 \\\\ 1 \\end{bmatrix} \\Rightarrow \\begin{bmatrix} 1 \\\\ 1 \\end{bmatrix}\n", "$$\n", "\n", "This transformation is often called **shear**, and the matrix is:\n", "\n", "\n", "$$ S = \\begin{bmatrix} 1 & 1 \\\\\n", " 0 & 1 \\end{bmatrix} $$\n", "\n", "The shear of any vector $\\mathbf{x}$ is the multiplication $S\\mathbf{x}$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's define these matrices as NumPy arrays, then use our helper function to visualize the corresponding transformation." ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 0 -1]\n", " [ 1 0]]\n" ] } ], "source": [ "rotation = numpy.array([[0,-1], [1,0]])\n", "print(rotation)" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[1 1]\n", " [0 1]]\n" ] } ], "source": [ "shear = numpy.array([[1,1], [0,1]])\n", "print(shear)" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_linear_transformation(shear)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Scaling\n", "\n", "A **scaling** transformation doesn't rotate or shear the basis vectors, but scales them in length. For example, a transformation that elongates $\\mathbf{i}$ but shrinks $\\mathbf{j}$ could do:\n", "\n", "\n", "$$\n", "\\mathbf{i} = \\begin{bmatrix} 1 \\\\ 0 \\end{bmatrix} \\Rightarrow \\begin{bmatrix} 2 \\\\ 0 \\end{bmatrix} \\\\\n", "\\mathbf{j} = \\begin{bmatrix} 0 \\\\ 1 \\end{bmatrix} \\Rightarrow \\begin{bmatrix} 0 \\\\ 0.5 \\end{bmatrix}\n", "$$\n", "\n", "Look at what the matrix transformation does in this case…" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[2. 0. ]\n", " [0. 0.5]]\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "scale = numpy.array([[2,0], [0,0.5]])\n", "print(scale)\n", "plot_linear_transformation(scale)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Identity\n", "\n", "The common structure of scaling matrices is that they have non-zero values in the diagonal, but zero values elsewhere.\n", "One special scaling matrix leaves the lengths of the basis vectors unchanged: it is called the **identity** matrix:\n", "\n", "\n", "$$ I = \\begin{bmatrix} 1 & 0 \\\\\n", " 0 & 1 \\end{bmatrix} $$\n", "\n", "NumPy creates identity arrays of any size with [`numpy.identity()`](https://docs.scipy.org/doc/numpy/reference/generated/numpy.eye.html?highlight=eye#numpy.eye), passing the dimension (number of rows and columns) as argument. In the 2D case:" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[1. 0.]\n", " [0. 1.]]\n" ] } ], "source": [ "I = numpy.identity(2)\n", "print(I)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Exercise:\n", "\n", "Create a rotation matrix that rotates every vector 90 degrees clockwise, then visualize the transformation with our helper function." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Matrix-matrix multiplication\n", "\n", "What do you think happens when we apply two linear transformations? For example, if we rotate all vectors by 90 degrees to the left, and *then* apply a shear transformation?\n", "\n", "Take any vector $\\mathbf{x}$, rotate it by multiplying it with the matrix $R$, then take this transformed vector and multiply it by the matrix $S$. The final vector is the result of the two combined linear transformations. It is analogous to the composition of two functions, and its computation leads to a matrix-matrix multiplication:\n", "\n", "$$\n", " S\\, R\\, \\mathbf{x} =\n", " \\begin{bmatrix} 1 & 1 \\\\\n", " 0 & 1 \\end{bmatrix}\n", " \\begin{bmatrix} 0 & -1 \\\\\n", " 1 & 0 \\end{bmatrix}\n", " \\mathbf{x}\n", "$$\n", "\n", "We can almost work this out in our heads. \n", "The unit vector $\\mathbf{i}$ gets first rotated to $\\begin{bmatrix} 0 \\\\ 1 \\end{bmatrix}$ (the first column of $R$), and then is transformed by $S$ via the multiplication:\n", "\n", "$$\n", " S\\,\\begin{bmatrix} 0 \\\\ 1 \\end{bmatrix} =\n", " \\begin{bmatrix} 1 & 1 \\\\\n", " 0 & 1 \\end{bmatrix}\n", " \\begin{bmatrix} 0 \\\\ 1 \\end{bmatrix} =\n", " 0 \\begin{bmatrix} 1 \\\\ 0 \\end{bmatrix}+\n", " 1 \\begin{bmatrix} 1 \\\\ 1 \\end{bmatrix} =\n", " \\begin{bmatrix} 1 \\\\ 1 \\end{bmatrix}\n", "$$\n", "\n", "Similarly for the unit vector $\\mathbf{j}$, we now find it lands on $\\begin{bmatrix} -1 \\\\ 0 \\end{bmatrix}$. We have the two columns of the resulting matrix from the multiplication $SR$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Python multiplies matrices\n", "\n", "Python (since version 3.5) has a **built-in operator** that computes matrix-matrix multiplication: `@`. Try it:" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 1 -1]\n", " [ 1 0]]\n" ] } ], "source": [ "print(shear@rotation)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Yep. Those are the two column vectors we worked out above. Beautiful. \n", "Let's visualize the combined transformation now." ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_linear_transformation(shear@rotation)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Key idea:\n", "\n", "> Matrix multiplication corresponds to composition of linear transformations, i.e., applying two transformations in sequence.\n", "\n", "This view of matrix multiplication will save you from a lot of unnecessary memorization. It also illuminates the properties of matrix multiplications. For example, is it the same to apply shear and *then* rotate, instead of the other way around? \n", "\n", "This is the same question as asking if matrix multiplication is commutative. Is $SR$ the same as $RS$?\n", "\n", "We have a helper function that plots the grid lines on a plane after two transformations in sequence. Let's try it with $S$ and $R$ in swapped orders." ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# the order of transformation: from right to left\n", "plot_linear_transformations(rotation, shear) " ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_linear_transformations(shear, rotation) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Nope. The result is not the same. The order of transformations matters and **matrix mulitiplication is not commutative** (in general).\n", "\n", "Episode four of the series [_\"Essence of Linear Algebra\"_](http://3b1b.co/eola) beautifully illustrates the key idea of matrix multiplication as composition of linear transformations [4]." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Inverse of a matrix\n", "\n", "Thinking of matrices as linear transformations also helps demistify the idea of an **inverse**. We won't go into details here, but imagine that you apply two transformations in sequence, and every vector in 2D space ends up just where it started. Well, that can happen when one transformation undoes the previous one. This means that the second transformation is the inverse of the first.\n", "\n", "NumPy has great built-in Linear Algebra capabilities in the `numpy.linalg` module. Among its many functions, we get [`inv()`](https://docs.scipy.org/doc/numpy-1.15.0/reference/generated/numpy.linalg.inv.html), to compute the inverse of a matrix. So we can try right away to visualize a sequence of transformations: first with the matrix $M$, then the inverse of $M$. Check it out." ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [], "source": [ "from numpy.linalg import inv" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "M = numpy.array([[1,2], [2,1]])\n", "M_inv = inv(M)\n", "plot_linear_transformations(M, M_inv)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The combined action of the linear transformation $M$ and its inverse $M^{-1}$ is to leave every vector the same. In other words, the matrix multiplication $M^{-1}M$ is equal to the identity $I$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## What we've learned\n", "\n", "- What is a vector.\n", "- The two fundamental vector operations: vector addition and scaling.\n", "- The concept of basis vectors.\n", "- Making a linear combination of vectors; the concept of span.\n", "- When a set of vectors is linearly independent.\n", "- A matrix is a linear transformation.\n", "- Matrix-vector multiplication: a combination of the matrix columns scaled by the vector components.\n", "- Some special transformations: rotation, shear, scaling, identity.\n", "- Matrix-matrix multiplication: composition of linear transformations.\n", "- Idea of the matrix inverse: the transformation that reverses the effect of another." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## References\n", "\n", "1. Vectors, what even are they? Essence of linear algebra, chapter 1. Video at https://youtu.be/fNk_zzaMoSs (2016), by Grant Sanderson.\n", "2. Linear combinations, span, and basis vectors. Essence of linear algebra, chapter 2. Video at https://youtu.be/k7RM-ot2NWY (2016), by Grant Sanderson.\n", "3. Linear transformations and matrices. Essence of linear algebra, chapter 3. Video at https://youtu.be/kYB8IZa5AuE (2016), by Grant Sanderson.\n", "4. Matrix multiplication as composition. Essence of linear algebra, chapter 4. Video at https://youtu.be/XkY2DOUCWMU (2016), by Grant Sanderson." ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Execute this cell to load the notebook's style sheet, then ignore it\n", "from IPython.core.display import HTML\n", "css_file = '../style/custom.css'\n", "HTML(open(css_file, \"r\").read())" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.7" } }, "nbformat": 4, "nbformat_minor": 2 }