{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"import sympy as sy\n",
"sy.init_printing() "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Null Space "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The _null space_, denoted as $\\text{Nul}A$ is the solution set of a homogeneous linear system, i.e. $Ax=0$. \n",
"\n",
"A null space is a always a subspace of $\\mathbb{R}^n$, why? Because one solution can always be the origin $(0, 0, ...)$.\n",
"\n",
"As an example, consider a linear system.\n",
"\n",
"$$\n",
"2x_1-x_2+x_3 = 0\\\\\n",
"x_1+2x_2+3x_3= 0 \n",
"$$\n",
"\n",
"The augmented matrix is \n",
"\n",
"$$\n",
"\\left[\n",
"\\begin{matrix}\n",
"2 & -1 & 1 & 0\\\\\n",
"1 & 2 & 3 & 0\n",
"\\end{matrix}\n",
"\\right]\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Before solving the system, we have already known there is no unique solution since a free variable presents, due to the fact that two equation with three variables.\n",
"\n",
"Solve for the reduced echelon form."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left( \\left[\\begin{matrix}1 & 0 & 1 & 0\\\\0 & 1 & 1 & 0\\end{matrix}\\right], \\ \\left( 0, \\ 1\\right)\\right)$"
],
"text/plain": [
"⎛⎡1 0 1 0⎤ ⎞\n",
"⎜⎢ ⎥, (0, 1)⎟\n",
"⎝⎣0 1 1 0⎦ ⎠"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Aug = sy.Matrix([[2,-1,1,0],[1,2,3,0]])\n",
"Aug.rref()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$x_3$ is a free variable, the solution set can be written as\n",
"\n",
"$$\n",
"\\left[\n",
"\\begin{matrix}\n",
"x_1 \\\\ x_2 \\\\ x_3\n",
"\\end{matrix}\n",
"\\right]=\n",
"\\left[\n",
"\\begin{matrix}\n",
"-x_3 \\\\ -x_3 \\\\ x_3\n",
"\\end{matrix}\n",
"\\right]=\n",
"x_3\\left[\n",
"\\begin{matrix}\n",
"-1 \\\\ -1 \\\\ 1\n",
"\\end{matrix}\n",
"\\right]\n",
"$$\n",
"\n",
"which is a line passing both origin $(0, 0, 0)$ and $(-1, -1, 1)$, also a subspace of $\\mathbb{R}^3$."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now consider another example, suppose we have an augmented matrix"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left[\\begin{matrix}-3 & 6 & -1 & 1 & -7 & 0\\\\1 & -2 & 2 & 3 & -1 & 0\\\\2 & -4 & 5 & 8 & -4 & 0\\end{matrix}\\right]$"
],
"text/plain": [
"⎡-3 6 -1 1 -7 0⎤\n",
"⎢ ⎥\n",
"⎢1 -2 2 3 -1 0⎥\n",
"⎢ ⎥\n",
"⎣2 -4 5 8 -4 0⎦"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Aug = sy.Matrix([[-3,6,-1,1,-7,0],[1,-2,2,3,-1,0],[2,-4,5,8,-4,0]]);Aug"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left( \\left[\\begin{matrix}1 & -2 & 0 & -1 & 3 & 0\\\\0 & 0 & 1 & 2 & -2 & 0\\\\0 & 0 & 0 & 0 & 0 & 0\\end{matrix}\\right], \\ \\left( 0, \\ 2\\right)\\right)$"
],
"text/plain": [
"⎛⎡1 -2 0 -1 3 0⎤ ⎞\n",
"⎜⎢ ⎥ ⎟\n",
"⎜⎢0 0 1 2 -2 0⎥, (0, 2)⎟\n",
"⎜⎢ ⎥ ⎟\n",
"⎝⎣0 0 0 0 0 0⎦ ⎠"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Aug.rref()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The solution can be written as:"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\n",
"\\left[\n",
"\\begin{matrix}\n",
"x_1 \\\\ x_2 \\\\ x_3 \\\\x_4 \\\\ x_5\n",
"\\end{matrix}\n",
"\\right]=\n",
"\\left[\n",
"\\begin{matrix}\n",
"2x_2+x_4-3x_5 \\\\ x_2 \\\\ -2x_4+2x_5 \\\\x_4 \\\\ x_5\n",
"\\end{matrix}\n",
"\\right]=\n",
"x_2\\left[\n",
"\\begin{matrix}\n",
"2 \\\\ 1 \\\\ 0 \\\\0 \\\\ 0\n",
"\\end{matrix}\n",
"\\right]\n",
"+\n",
"x_4\\left[\n",
"\\begin{matrix}\n",
"1 \\\\ 0 \\\\ -2 \\\\1 \\\\ 0\n",
"\\end{matrix}\n",
"\\right]\n",
"+x_5\\left[\n",
"\\begin{matrix}\n",
"-3 \\\\ 0 \\\\ 2 \\\\0 \\\\ 1\n",
"\\end{matrix}\n",
"\\right]\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The $\\text{Nul}A$ is a subspace in $\\mathbb{R}^5$ with $\\text{dim}A=3$. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Null Space vs Col Space "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Consider matrix $A$"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left[\\begin{matrix}2 & 4 & -2 & 1\\\\-2 & -5 & 7 & 3\\\\3 & 7 & -8 & 6\\end{matrix}\\right]$"
],
"text/plain": [
"⎡2 4 -2 1⎤\n",
"⎢ ⎥\n",
"⎢-2 -5 7 3⎥\n",
"⎢ ⎥\n",
"⎣3 7 -8 6⎦"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"A = sy.Matrix([[2,4,-2,1],[-2,-5,7,3],[3,7,-8,6]]);A"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Column space is a subspace in $\\mathbb{R}^n$, what is $n$? It is the number of rows, $n=3$.\n",
"\n",
"Null space is a subspace in $\\mathbb{R}^m$, what is $m$? It is the number of columns, $m=4$."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"How to find any nonzero vector in $\\text{Col}A$ and in $\\text{Nul}A$?\n",
"\n",
"Any column in a matrix can be a nonzero vector in $\\text{Col}A$, for instance first column: $(2, -2, 3)^T$."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"But to find a nonzero vector in null space requires some effort, construct the augmented matrix then turn it into rref."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left( \\left[\\begin{matrix}1 & 0 & 9 & 0 & 0\\\\0 & 1 & -5 & 0 & 0\\\\0 & 0 & 0 & 1 & 0\\end{matrix}\\right], \\ \\left( 0, \\ 1, \\ 3\\right)\\right)$"
],
"text/plain": [
"⎛⎡1 0 9 0 0⎤ ⎞\n",
"⎜⎢ ⎥ ⎟\n",
"⎜⎢0 1 -5 0 0⎥, (0, 1, 3)⎟\n",
"⎜⎢ ⎥ ⎟\n",
"⎝⎣0 0 0 1 0⎦ ⎠"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Aug = sy.Matrix([[2,4,-2,1,0],[-2,-5,7,3,0],[3,7,-8,6,0]]);Aug.rref()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The solution set with a free variable $x_3$ (because column 3 has no pivot) is \n",
"\n",
"$$\n",
"\\left[\n",
"\\begin{matrix}\n",
"x_1 \\\\ x_2 \\\\ x_3\\\\x_4\n",
"\\end{matrix}\n",
"\\right]=\n",
"\\left[\n",
"\\begin{matrix}\n",
"-9x_3 \\\\ 5x_3 \\\\ x_3\\\\0\n",
"\\end{matrix}\n",
"\\right]\n",
"$$\n",
"\n",
"If we pick $x_3 =1$, a nonzero vector in $\\text{Nul}A$ is $(-9, 5, 1, 0)^T$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now consider two vectors\n",
"\n",
"$$\n",
"u = \\left[\n",
"\\begin{matrix}\n",
"3 \\\\ -2 \\\\ -1\\\\ 0 \n",
"\\end{matrix}\n",
"\\right],\\qquad\n",
"v = \\left[\n",
"\\begin{matrix}\n",
"3 \\\\ -1\\\\3\n",
"\\end{matrix}\n",
"\\right]\\\\\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Is $u$ in $\\text{Nul}A$? It can be verified easily"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left[\\begin{matrix}0\\\\-3\\\\3\\end{matrix}\\right]$"
],
"text/plain": [
"⎡0 ⎤\n",
"⎢ ⎥\n",
"⎢-3⎥\n",
"⎢ ⎥\n",
"⎣3 ⎦"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"u = sy.Matrix([[3],[-2],[-1],[0]])\n",
"A*u"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$Au\\neq \\mathbf{0}$, therefore $u$ is not in $\\text{Nul}A$."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Is $v$ in $\\text{Col}A$? Construct an augmented matrix with $v$, then solve it"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left( \\left[\\begin{matrix}1 & 0 & 9 & 0 & 5\\\\0 & 1 & -5 & 0 & - \\frac{30}{17}\\\\0 & 0 & 0 & 1 & \\frac{1}{17}\\end{matrix}\\right], \\ \\left( 0, \\ 1, \\ 3\\right)\\right)$"
],
"text/plain": [
"⎛⎡1 0 9 0 5 ⎤ ⎞\n",
"⎜⎢ ⎥ ⎟\n",
"⎜⎢ -30 ⎥ ⎟\n",
"⎜⎢0 1 -5 0 ────⎥, (0, 1, 3)⎟\n",
"⎜⎢ 17 ⎥ ⎟\n",
"⎜⎢ ⎥ ⎟\n",
"⎝⎣0 0 0 1 1/17⎦ ⎠"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"v = sy.Matrix([[3],[-1],[3]])\n",
"A.row_join(v).rref()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The augmented matrix show there are solutions, i.e. $v$ is a linear combination of its column space basis, so $v$ is in $\\text{Col}A$."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Row Space "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The **Row space** denoted as $\\text{Row}A$, contains all linear combination of row vectors and subspace in $\\mathbb{R}^n$."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"If we perform row operations on $A$ to obtain $B$, both matrices have the same row space, because $B$'s rows are linear combinations of $A$'s. However, row operation will change the row dependence. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## An Example "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Find the row, column and null space of "
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left[\\begin{matrix}-2 & -5 & 8 & 0 & -17\\\\1 & 3 & -5 & 1 & 5\\\\3 & 11 & -19 & 7 & 1\\\\1 & 7 & -13 & 5 & -3\\end{matrix}\\right]$"
],
"text/plain": [
"⎡-2 -5 8 0 -17⎤\n",
"⎢ ⎥\n",
"⎢1 3 -5 1 5 ⎥\n",
"⎢ ⎥\n",
"⎢3 11 -19 7 1 ⎥\n",
"⎢ ⎥\n",
"⎣1 7 -13 5 -3 ⎦"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"A = sy.Matrix([[-2, -5, 8, 0, -17],\n",
" [1, 3, -5, 1, 5], \n",
" [3, 11, -19, 7, 1], \n",
" [1, 7, -13, 5, -3]]);A"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left( \\left[\\begin{matrix}1 & 0 & 1 & 0 & 1\\\\0 & 1 & -2 & 0 & 3\\\\0 & 0 & 0 & 1 & -5\\\\0 & 0 & 0 & 0 & 0\\end{matrix}\\right], \\ \\left( 0, \\ 1, \\ 3\\right)\\right)$"
],
"text/plain": [
"⎛⎡1 0 1 0 1 ⎤ ⎞\n",
"⎜⎢ ⎥ ⎟\n",
"⎜⎢0 1 -2 0 3 ⎥ ⎟\n",
"⎜⎢ ⎥, (0, 1, 3)⎟\n",
"⎜⎢0 0 0 1 -5⎥ ⎟\n",
"⎜⎢ ⎥ ⎟\n",
"⎝⎣0 0 0 0 0 ⎦ ⎠"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"B = A.rref();B"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The basis of the row space of $B$ is its first 3 rows: $(1,0,1,0,1), (0, 1, -2, 0, 3), (0, 0, 0, 1, -5)$ which are also the basis of the row space of $A$. However it does not necessarily mean that first 3 rows of $A$ forms the basis for row space, because the dependence among rows changed by row operation."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In constrast, the basis of col space of $A$ is $(-2, 1, 3, 1)^T, (-5, 3, 11, 7)^T, (0, 1, 7, 5)^T$."
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left( \\left[\\begin{matrix}1 & 0 & 1 & 0 & 1 & 0\\\\0 & 1 & -2 & 0 & 3 & 0\\\\0 & 0 & 0 & 1 & -5 & 0\\\\0 & 0 & 0 & 0 & 0 & 0\\end{matrix}\\right], \\ \\left( 0, \\ 1, \\ 3\\right)\\right)$"
],
"text/plain": [
"⎛⎡1 0 1 0 1 0⎤ ⎞\n",
"⎜⎢ ⎥ ⎟\n",
"⎜⎢0 1 -2 0 3 0⎥ ⎟\n",
"⎜⎢ ⎥, (0, 1, 3)⎟\n",
"⎜⎢0 0 0 1 -5 0⎥ ⎟\n",
"⎜⎢ ⎥ ⎟\n",
"⎝⎣0 0 0 0 0 0⎦ ⎠"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Aug = A.row_join(sy.zeros(4,1));Aug.rref()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The null space is \n",
"\n",
"$$\n",
"\\left[\n",
"\\begin{matrix}\n",
"x_1 \\\\ x_2 \\\\ x_3\\\\x_4 \\\\x_5\n",
"\\end{matrix}\n",
"\\right]=\n",
"\\left[\n",
"\\begin{matrix}\n",
"-x_3-x_5 \\\\ 2x_3-3x_5 \\\\ x_3\\\\5x_5 \\\\x_5\n",
"\\end{matrix}\n",
"\\right]=\n",
"x_3\\left[\n",
"\\begin{matrix}\n",
"-1 \\\\ 2 \\\\ 1\\\\0 \\\\0\n",
"\\end{matrix}\n",
"\\right]+\n",
"x_5\n",
"\\left[\n",
"\\begin{matrix}\n",
"-1 \\\\ -3 \\\\ 0\\\\5 \\\\1\n",
"\\end{matrix}\n",
"\\right]\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Rank "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Definition of rank:\n",
"The _rank_ is the dimension of the column space of $A$. The _nullity_ of $A$ is the dimension of the null space."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## The Rank Theorem"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The dimensions of the column space and the row space of an $m \\times n$ matrix $A$ are equal. Therefore, the rank is the same for either column space and row space.\n",
"\n",
"This common dimension, the rank of $A$, also equals the number of pivot positions in $A$ and satisfies the equation:\n",
"$$\n",
"\\operatorname{rank} A + \\operatorname{dim} \\mathrm{Nul} A = n\n",
"$$\n",
"\n",
"The intuition behind this is that when a matrix $A$ is converted into its reduced row echelon form (rref) $B$, we can indirectly determine the basis of the column space by matching the columns of $B$ with those of $A$. The columns in $A$ that correspond to pivot columns in $B$ form the basis of the column space.\n",
"\n",
"In the rref, we can also directly see the basis of the row space. Each row in the basis of the row space must contain a pivot. The rows that do not contain pivots correspond to the free variables, which determine the dimension of the null space."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 1 "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"If $A$ is $45 \\times 50$ matrix with a $10$-dimension nullity, what is the rank of $A$?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$10$-$D$ nullity means 10 free variables, so the pivots are $50-10=40$, which is also the rank of $A$."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 2 "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The matrices below are row equivalent.\n",
"$$\n",
"A=\\left[\\begin{array}{rrrrr}\n",
"2 & -1 & 1 & -6 & 8 \\\\\n",
"1 & -2 & -4 & 3 & -2 \\\\\n",
"-7 & 8 & 10 & 3 & -10 \\\\\n",
"4 & -5 & -7 & 0 & 4\n",
"\\end{array}\\right], \\quad B=\\left[\\begin{array}{rrrrr}\n",
"1 & -2 & -4 & 3 & -2 \\\\\n",
"0 & 3 & 9 & -12 & 12 \\\\\n",
"0 & 0 & 0 & 0 & 0 \\\\\n",
"0 & 0 & 0 & 0 & 0\n",
"\\end{array}\\right]\n",
"$$\n",
"1. Find rank $A$ and $\\operatorname{dim}$ Nul $A$\n",
"2. Find bases for Col $A$ and Row $A$.\n",
"3. What is the next step to perform to find a basis for Nul $A$ ?\n",
"4. How many pivot columns are in a row echelon form of $A^{T} ?$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"1. $rank(A)=2$, because $B$ has two pivots. And nullity is the number of free variables, there are 3, so $\\text{dim Nul}A = 3$. "
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left( \\left[\\begin{matrix}1 & 0 & 2 & -5 & 6 & 0\\\\0 & 1 & 3 & -4 & 4 & 0\\\\0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0\\end{matrix}\\right], \\ \\left( 0, \\ 1\\right)\\right)$"
],
"text/plain": [
"⎛⎡1 0 2 -5 6 0⎤ ⎞\n",
"⎜⎢ ⎥ ⎟\n",
"⎜⎢0 1 3 -4 4 0⎥ ⎟\n",
"⎜⎢ ⎥, (0, 1)⎟\n",
"⎜⎢0 0 0 0 0 0⎥ ⎟\n",
"⎜⎢ ⎥ ⎟\n",
"⎝⎣0 0 0 0 0 0⎦ ⎠"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"A = sy.Matrix([[2,-1,1,-6,8,0],\n",
" [1,-2,-4,3,-2,0],\n",
" [-7,8,10,3,-10,0],\n",
" [4,-5,-7,0,4,0]])\n",
"A.rref()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"2. Bases for $\\text{Col}A$ is $(2,1,-7,4)^T, (-1,-2,8,-5)^T$, and for $\\text{Row}A$ is $(1,-2,-4,3,-2),(0,3,9,-12,12)$."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The $\\text{Nul}A$ and basis is\n",
"\n",
"$$\n",
"\\left[\n",
"\\begin{matrix}\n",
"x_1 \\\\ x_2 \\\\ x_3\\\\x_4 \\\\x_5\n",
"\\end{matrix}\n",
"\\right]=\n",
"\\left[\n",
"\\begin{matrix}\n",
"-2x_3+5x_4-6x_5 \\\\ -3x_3+4x_4-4x_5 \\\\ x_3\\\\x_4 \\\\x_5\n",
"\\end{matrix}\n",
"\\right]=\n",
"x_3\n",
"\\left[\n",
"\\begin{matrix}\n",
"-2 \\\\ -3 \\\\ 1\\\\0 \\\\0\n",
"\\end{matrix}\n",
"\\right]+\n",
"x_4\n",
"\\left[\n",
"\\begin{matrix}\n",
"5 \\\\ 4 \\\\ 0\\\\1 \\\\0\n",
"\\end{matrix}\n",
"\\right]+\n",
"x_5\n",
"\\left[\n",
"\\begin{matrix}\n",
"-6 \\\\ -4 \\\\ 0\\\\0 \\\\1\n",
"\\end{matrix}\n",
"\\right]\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"3. Perform rref on augmented $A$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"4. Transpose $A$ then do rref."
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left( \\left[\\begin{matrix}1 & 0 & -2 & 1\\\\0 & 1 & -3 & 2\\\\0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0\\end{matrix}\\right], \\ \\left( 0, \\ 1\\right)\\right)$"
],
"text/plain": [
"⎛⎡1 0 -2 1⎤ ⎞\n",
"⎜⎢ ⎥ ⎟\n",
"⎜⎢0 1 -3 2⎥ ⎟\n",
"⎜⎢ ⎥ ⎟\n",
"⎜⎢0 0 0 0⎥ ⎟\n",
"⎜⎢ ⎥, (0, 1)⎟\n",
"⎜⎢0 0 0 0⎥ ⎟\n",
"⎜⎢ ⎥ ⎟\n",
"⎜⎢0 0 0 0⎥ ⎟\n",
"⎜⎢ ⎥ ⎟\n",
"⎝⎣0 0 0 0⎦ ⎠"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"A.T.rref()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"There are 2 pivot columns."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Actually, we don't need any calculation to know the rank of $A^T$, because\n",
"\n",
"$$\n",
"rank(A)=rank(A^T)\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Orthogonality of $\\text{Nul}A$ and $\\text{Row}A$ "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## $\\text{Nul}A \\perp \\text{Row}A$ "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here is the intersting connections of these subspaces we have discussed. Consider"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left[\\begin{matrix}5 & 8 & 2\\\\10 & 16 & 4\\\\3 & 4 & 1\\end{matrix}\\right]$"
],
"text/plain": [
"⎡5 8 2⎤\n",
"⎢ ⎥\n",
"⎢10 16 4⎥\n",
"⎢ ⎥\n",
"⎣3 4 1⎦"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"A = sy.Matrix([[5, 8, 2], [10, 16, 4], [3, 4, 1]]);A"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left( \\left[\\begin{matrix}1 & 0 & 0\\\\0 & 1 & \\frac{1}{4}\\\\0 & 0 & 0\\end{matrix}\\right], \\ \\left( 0, \\ 1\\right)\\right)$"
],
"text/plain": [
"⎛⎡1 0 0 ⎤ ⎞\n",
"⎜⎢ ⎥ ⎟\n",
"⎜⎢0 1 1/4⎥, (0, 1)⎟\n",
"⎜⎢ ⎥ ⎟\n",
"⎝⎣0 0 0 ⎦ ⎠"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"A.rref()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The basis of row space of $A$ is $(1, 0, 0)$ and $(0, 1, .25)$.And the $\\text{Row}A$ is \n",
"\n",
"$$\n",
"\\text{Row}A=\n",
"s\\left[\n",
"\\begin{matrix}\n",
"1 \\\\ 0\\\\ 0\n",
"\\end{matrix}\n",
"\\right]+\n",
"t\\left[\n",
"\\begin{matrix}\n",
"0 \\\\ 1\\\\ 0.25\n",
"\\end{matrix}\n",
"\\right]\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The $\\text{Nul}A$ is \n",
"$$\n",
"\\left[\n",
"\\begin{matrix}\n",
"x_1 \\\\ x_2\\\\ x_3\n",
"\\end{matrix}\n",
"\\right]=\n",
"x_3\n",
"\\left[\n",
"\\begin{matrix}\n",
"0 \\\\ -.25\\\\ 1\n",
"\\end{matrix}\n",
"\\right]\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we can visualize their relations geometrically. Again keep in mind that Matplotlib does not render 3D properly, so you need some imagination as well.\n",
"\n",
"Here is what we observe. \n",
"\n",
"The $\\text{Row}A$ is a plane and $\\text{Nul}A$ is a line which is perpendicular to the plane (maybe 3D plot not so obvious about it). It is easy to grasp the idea if you notice that in a homogeneous system $Ab = \\mathbf{0}$, it breaks down into dot products\n",
"\n",
"$$\n",
"Ab =\\left[\n",
"\\begin{matrix}\n",
"A_{1\\cdot}\\cdot b \\\\ A_{2\\cdot}\\cdot b\\\\ A_{3\\cdot}\\cdot b \n",
"\\end{matrix}\n",
"\\right] \n",
"=\n",
"\\left[\n",
"\\begin{matrix}\n",
"0 \\\\ 0 \\\\ 0\n",
"\\end{matrix}\n",
"\\right] \n",
"$$\n",
"\n",
"where $A_{1\\cdot}, A_{2\\cdot}, A_{3\\cdot}$ are the rows of $A$. In later chapters we will prove when the dot product of two vectors equals zero, they are geometrically perpendicular."
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/plain": [
"