{
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      "source": [
        "# Working with two-dimensional arrays\n",
        "\n",
        "<hr>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
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      "source": [
        "import numpy as np"
      ]
    },
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      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "<hr>\n",
        "\n",
        "Numpy enables you do to matrix calculations on two-dimensional arrays. In exercise, you will practice doing matrix calculations on arrays. We'll start by making a matrix and a vector to practice with. You can copy and paste the code below."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "tags": []
      },
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      "source": [
        "A = np.array(\n",
        "    [\n",
        "        [6.7, 1.3, 0.6, 0.7],\n",
        "        [0.1, 5.5, 0.4, 2.4],\n",
        "        [1.1, 0.8, 4.5, 1.7],\n",
        "        [0.0, 1.5, 3.4, 7.5],\n",
        "    ]\n",
        ")\n",
        "\n",
        "b = np.array([1.1, 2.3, 3.3, 3.9])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "**a)** First, let's practice slicing.\n",
        "\n",
        "1. Print row 1 (remember, indexing starts at zero) of `A`.\n",
        "2. Print columns 1 and 3 of `A`.\n",
        "3. Print the values of every entry in `A` that is greater than 2.\n",
        "4. Print the diagonal of `A`. using the `np.diag()` function.\n",
        "\n",
        "**b)** The `np.linalg` module has some powerful linear algebra tools. \n",
        "\n",
        "1. First, we'll solve the linear system $\\mathsf{A}\\cdot \\mathbf{x} = \\mathbf{b}$. Try it out: use `np.linalg.solve()`. Store your answer in the Numpy array `x`.\n",
        "2. Now do `np.dot(A, x)` to verify that $\\mathsf{A}\\cdot \\mathbf{x} = \\mathbf{b}$.\n",
        "3. Use `np.transpose()` to compute the transpose of `A`.\n",
        "4. Use `np.linalg.inv()` to compute the inverse of `A`.\n",
        "\n",
        "**c)** Sometimes you want to convert a two-dimensional array to a one-dimensional array. This can be done with `np.ravel()`. \n",
        "\n",
        "1. See what happens when you do `B = np.ravel(A)`.\n",
        "2. Look of the documentation for `np.reshape()`. Then, reshape `B` to make it look like `A` again."
      ]
    },
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      "source": [
        "<br />"
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