04_Lecture_I_01_Geometric_view_of_linear_algebra.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "+ This notebook is part of the lecture **GEOMETRIC VIEW OF LINEAR ALGEBRA** in the OCW MIT course 18.06 by Prof Gilbert Strang [1]\n",
    "+ Created Dr J H Klopper\n",
    "    + Associate Professor\n",
    "    + Department of Biostatistics and Bioinformatics\n",
    "    + Milken Institute School of Public Health\n",
    "    + The George Washington University\n",
    "    + <a href=\"mailto:juanklopper@gwu.edu\">Email me with your thoughts, comments, suggestions and corrections</a> \n",
    "<a rel=\"license\" href=\"http://creativecommons.org/licenses/by-nc/4.0/\"><img alt=\"Creative Commons Licence\" style=\"border-width:0\" src=\"https://i.creativecommons.org/l/by-nc/4.0/88x31.png\" /></a><br /><span xmlns:dct=\"http://purl.org/dc/terms/\" href=\"http://purl.org/dc/dcmitype/InteractiveResource\" property=\"dct:title\" rel=\"dct:type\">Linear Algebra OCW MIT18.06</span> <span xmlns:cc=\"http://creativecommons.org/ns#\" property=\"cc:attributionName\">Jupyter notebook study notes by Dr Juan H Klopper</span> is licensed under a <a rel=\"license\" href=\"http://creativecommons.org/licenses/by-nc/4.0/\">Creative Commons Attribution-NonCommercial 4.0 International License</a>.\n",
    "\n",
    "+ [1] <a href=\"https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010/video_galleries/video-lectures/\">OCW MIT 18.06</a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![GWU LOGO](GWU_Logo_Horizontal.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Geometrical view"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Preamble"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The initial exploration of linear algebra is done in the context of linear equations and vectors in two- and three-dimensional space.  This is a geometrical view of linear algebra."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## System of linear equations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Most courses and textbooks introduce linear algebra as a method of solving systems of linear equations.  <span style=\"color:green\"><b>Linear equations</b></span> have variables that are each of power one, do not multiply or divide each other, are not transformed by trigonometric, exponential, and logarithmic functions, and are not part of derivatives, integrals, or any othe roperations.  Examples are shown in (1) below."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$ \\begin{align} {2x}-{y}&={3} \\\\ -{x} + 2{y} &= {0} \\end{align} \\tag{1} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style=\"color:green\"><b>System of linear equations</b></span> or <span style=\"color:green\"><b>linear system</b></span> is a collection of linear equations involving the same set of variables. Solving systems of linear equations attempts at finding numerical solutions for the variables that solve all the equations in the linear system.  A solution to (1) is shown in (2) below."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\begin{align}2 &\\left( 2 \\right) - 1 \\left( 1 \\right) = 3 \\\\ - &\\left( 2 \\right) + 2 \\left( 1 \\right) = 0\\end{align}\\tag{2}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We note from (2) that $x=2$ and $y=1$. This is the solution to the linear system in (1).  The solution to a linear system is the set of values for the variables that satisfies all the equations in the linear system.  The solution to a linear system is also called a <span style=\"color:green\"><b>root</b></span> or <span style=\"color:green\"><b>solution set</b></span>."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The linear system in (1) can be written as a matrix using only the coefficients of the variables toghether with the constants on the right-hand side of the equations. Such a matrix that includes the right-hand side constants is termed an <span style=\"color:green\"><b>augmented matrix</b></span>."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can create an augmented matrix from the system in (1).  To do this, we create a matrix of coefficients, including those from both sides of the equations.  We store the matrix as a computer variable called `A_augm` using the `Matrix` function from the `sympy` package, which we import in the code cell below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy import Matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}2 & -1 & 3\\\\-1 & 2 & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[ 2, -1, 3],\n",
       "[-1,  2, 0]])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A_augm = Matrix([[2, -1, 3], [-1, 2, 0]]) # Note the placement of ()'s and []'s\n",
    "A_augm # A_augm is a computer variable that contains the matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With two equations and two unknowns (variables $x$ and $y$), together with the right-hand side constants, we see an array of values along two rows and three columns, written in a set of brackets. Some textbooks use parentheses instead of brackets."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Because `A_augm` was created using the `Matrix()` function from `sympy`, it is an instance of this type.  The `type()` indicates it more specificically as a _mutable, dense matrix_."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "sympy.matrices.dense.MutableDenseMatrix"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# We can ask python what type of computer variable A_augm holds\n",
    "type(A_augm)  # We see that it is a mutable dense matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Mutable means that we can change the values of the elements (coefficients in this case) and dense because the value of each position in the matrix is stored.  (When there are many zeros, a sparse matrix can be created, that only stores the values that are not zero and their positions.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also create a <span style=\"color:green\"><b>matrix of coefficients</b></span>.  It includes only the left-hand side coefficients and because there are two equations and two unknows, the result is a matrix along two rows and two columns. We state the the shape of the matrix is $2 \\times 2$. We create the matrix of coefficients for the linear system in (1) using the `Matrix` function and assign the matrix to the variable `A`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}2 & -1\\\\-1 & 2\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[ 2, -1],\n",
       "[-1,  2]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = Matrix([[2, -1], [-1, 2]])  # Matrix of coefficients\n",
    "A"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The variables (unknowns) can be expressed as a column vector, saved as the computer variable `x_vect` below.  First, we specify the variable `x`, and `y` as mathematical variables using the `symbols` function, which we import below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy import symbols"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We create the mathematical variable $x$ and $y$ and assign them to the computer variable `x` and `y`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "x, y = symbols('x y') # Creating symbolic mathematical variables as opposed to computer variables\n",
    "# These symbols can no longer be used as computer variable names"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}x\\\\y\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[x],\n",
       "[y]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_vect = Matrix([x, y])\n",
    "x_vect"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The same goes for the column vector of solutions, saved as the computer variable `b_vect`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}3\\\\0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[3],\n",
       "[0]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b_vect = Matrix([3, 0])\n",
    "b_vect"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In (3) we see the matrix times the column vector results in the vector of solutions.  The (row, column) sizes are also shown. Note that matrices are ususally written as uppercase letters and that vector are written as lowercase letters in bold-face type."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$ \\begin{align} A_{2 \\times 2} \\quad \\mathbf{x}_{2 \\times 1} = \\mathbf{b}_{2 \\times 1} \\\\ \\\\ \\begin{bmatrix} 2 && -1 \\\\ -1 && 2 \\end{bmatrix} \\begin{bmatrix} x \\\\ y\\end{bmatrix} = \\begin{bmatrix} 3 \\\\ 0 \\end{bmatrix} \\end{align} \\tag{3}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since we created the matrix of coefficients `A` and the vector of unknowns `x_vect`, we can use Python to show the result of this multiplication."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}2 x - y\\\\- x + 2 y\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[ 2*x - y],\n",
       "[-x + 2*y]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A * x_vect # Matrix multiplication"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The result is the left-hand side of the linear system in (1)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `Eq` function in `sympy` is used below to create the matrix times the vector on the left-hand side (resulting in a column vector) and the solution vector on the right.  It gives a visual idea of how we use linear algebra to solve these systems."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy import Eq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}2 x - y\\\\- x + 2 y\\end{matrix}\\right] = \\left[\\begin{matrix}3\\\\0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Eq(Matrix([\n",
       "[ 2*x - y],\n",
       "[-x + 2*y]]), Matrix([\n",
       "[3],\n",
       "[0]]))"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Eq(A * x_vect, b_vect) # From Ax = b\n",
    "# The Eq function takes the arguments left-hand-side (LHS), right-handside (RHS) of the equation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The row picture"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Each linear equation in (1) is an equation of a straight line.  This represents the __row picture__ of a linear system.  The solutions to both equations is at the point where the lines in the plane intersect.  Take a look at the plot below. Don't be too concerned about the code for plotting.  It does not form part of this series of notebooks."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_vals = np.linspace(-3, 3, 100) # Create 100 values between -3 and 3\n",
    "# Note that we cannot use the computer variable x, because it has been reserved above as a mathematical variable in\n",
    "# the symbols function\n",
    "plt.figure(figsize = (10,8)) # Create a graph of size 10 by 8\n",
    "plt.plot(x_vals, 2 * x_vals - 3) # Plot every single value created above with 2 times that values\n",
    "# Taken from the first equation which was y = 2x or f(x) = 2x\n",
    "# The plot takes the arguments (code between parentheses) of x,y\n",
    "plt.plot(x_vals, ((x_vals / 2))) # Also plot the second equation\n",
    "plt.grid(True) # Add a grid to the plot\n",
    "# Set the x limits to -1 and 3\n",
    "plt.xlim([-1, 3]) # Set the x limits to -1 and 4\n",
    "#Set the y limit to -6 to 3\n",
    "plt.ylim([-6, 3]) # Set the y limit to -6 to 3\n",
    "# Remove the spines\n",
    "ax = plt.gca() # Get current axes\n",
    "ax.spines['top'].set_visible(False) # Remove top spine\n",
    "ax.spines['right'].set_visible(False) # Remove right spine\n",
    "ax.spines['bottom'].set_position('zero') # Move bottom spine to zero\n",
    "ax.spines['left'].set_position('zero') # Move left spine to zero\n",
    "# Add a horizontal line at y = 0\n",
    "plt.axhline(y = 0, color = 'k') # Add a horizontal line at y = 0\n",
    "# Add a vertical line at x = 0\n",
    "plt.axvline(x = 0, color = 'k') # Add a vertical line at x = 0\n",
    "# Add the equations to the plot\n",
    "plt.text(1, 1, r'$y = 2x - 3$', fontsize = 12) # Add the first equation\n",
    "plt.text(2.6, 0.7, r'$y = \\frac{x}{2}$', fontsize = 12) # Add the second equation\n",
    "plt.show; # Draw the plot on screen"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We note that the two line intersect at the point $\\left( 2, 1 \\right)$.  It should be clear that there are three possible outcomes for a system with two variables and two equations.  Either the lines intersect with a single solution, or they do not intersect at all (parallel lines), with no solutions, or they coincide, with infinitely many solutions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The column picture"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can view the same system as a vector problem.  Here the coefficients of each separate variable as a column vector.  This problem now becomes a linear combination of vectors.  We are thus asking how many (scalar multiplication) of one vector plus how many of the other vector will equal the vector on the right hand side.  This should be clear from (4) below."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$ x\\begin{bmatrix} 2 \\\\ -1 \\end{bmatrix}+y\\begin{bmatrix} -1 \\\\ 2 \\end{bmatrix}=\\begin{bmatrix} 3 \\\\ 0 \\end{bmatrix} \\tag{4}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As before, we create separate computer variables and show that the end-result is the same."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}2\\\\-1\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[ 2],\n",
       "[-1]])"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_var_vect = Matrix([2, -1])\n",
    "x_var_vect"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}-1\\\\2\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[-1],\n",
       "[ 2]])"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_var_vect = Matrix([-1, 2])\n",
    "y_var_vect"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}2 x - y\\\\- x + 2 y\\end{matrix}\\right] = \\left[\\begin{matrix}3\\\\0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Eq(Matrix([\n",
       "[ 2*x - y],\n",
       "[-x + 2*y]]), Matrix([\n",
       "[3],\n",
       "[0]]))"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Eq(x * x_var_vect + y * y_var_vect, b_vect)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the image below, we see the two vectors (blue and green) and the resultant vector (orange)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = plt.axes()\n",
    "\n",
    "ax.arrow(0.0, 0.0, 2.0, -1.0,\n",
    "        length_includes_head=True,\n",
    "        head_width=0.5,\n",
    "         head_length=0.7,\n",
    "         fc='lightblue',\n",
    "         ec='black')\n",
    "ax.arrow(0.0, 0.0, -1.0, 2.0,\n",
    "        length_includes_head=True,\n",
    "        head_width=0.5,\n",
    "        head_length=0.7,\n",
    "        fc='lightgreen',\n",
    "        ec='black')\n",
    "ax.arrow(0.0, 0.0, 3.0, 0.0,\n",
    "        length_includes_head=True,\n",
    "        head_width=0.5,\n",
    "         head_length=0.7,\n",
    "         fc='orange',\n",
    "         ec='black')\n",
    "\n",
    "plt.grid()\n",
    "\n",
    "plt.xlim(-5,5)\n",
    "plt.ylim(-5,5)\n",
    "\n",
    "plt.title('Vector view',fontsize=10)\n",
    "\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We know that it takes twice the blue vector and one time the green vector to give us the orange vector."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = plt.axes()\n",
    "\n",
    "ax.arrow(0.0, 0.0, 2.0, -1.0,\n",
    "        length_includes_head=True,\n",
    "        head_width=0.5,\n",
    "         head_length=0.7,\n",
    "         fc='lightblue',\n",
    "         ec='black')\n",
    "ax.arrow(2.0, -1.0, 2.0, -1.0,\n",
    "        length_includes_head=True,\n",
    "        head_width=0.5,\n",
    "         head_length=0.7,\n",
    "         fc='lightblue',\n",
    "         ec='black')\n",
    "\n",
    "ax.arrow(4.0, -2.0, -1.0, 2.0,\n",
    "        length_includes_head=True,\n",
    "        head_width=0.5,\n",
    "        head_length=0.7,\n",
    "        fc='lightgreen',\n",
    "        ec='black')\n",
    "ax.arrow(0.0, 0.0, 3.0, 0.0,\n",
    "        length_includes_head=True,\n",
    "        head_width=0.5,\n",
    "         head_length=0.7,\n",
    "         fc='orange',\n",
    "         ec='black')\n",
    "\n",
    "plt.grid()\n",
    "\n",
    "plt.xlim(-5,5)\n",
    "plt.ylim(-5,5)\n",
    "\n",
    "plt.title('Vector view',fontsize=10)\n",
    "\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It should be very clear that the two vectors are special in that linear combinations of them will allow us to fill a plane in $\\mathbb{R}^{2}$ (in which they both lie)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It should also be clear to see that these two vectors are not linear combinations of each other.  If this were so, they are linearly independent and linear combinations of them fill only a line in $\\mathbb{R}$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can imagine that the $xy$-plane is filled with (all the points are created by) vectors, i.e. I can find any coordinate by drawing a vector to it.  All these vectors together can be called a _set_ and they fill $\\mathbb{R}^{2}$.  Later we will learn about _basis vectors_ and how they _span_ a space."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The 3-space picture"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To end this section, we take a look at the three equation with three variables."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$ \\begin{align} {3x}+{2y}-{z}&=2 \\\\ {x}-{2y}-{z}&=3 \\\\ {2x}+{y}-{z}&={1} \\end{align} \\tag{5}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can create an augmented matrix from the coefficents, stored in the computer variable `A_augm` below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}3 & 2 & -1 & 2\\\\1 & -2 & -1 & 3\\\\2 & 1 & -1 & 1\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[3,  2, -1, 2],\n",
       "[1, -2, -1, 3],\n",
       "[2,  1, -1, 1]])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A_augm = Matrix([[3, 2, -1, 2], [1, -2, -1, 3], [2, 1, -1, 1]])\n",
    "A_augm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `.rref()` method will quickly solve the linear system for use."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(Matrix([\n",
       " [1, 0, 0,  5/2],\n",
       " [0, 1, 0, -3/2],\n",
       " [0, 0, 1,  5/2]]), (0, 1, 2))"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A_augm.rref()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The solution is where three planes in $\\mathbb{R}^{3}$ _cross_.  We can once again imagine that the planes (each equation) may never cross or lie on-top of each other.  Below is an image of three planes crossing at one point."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy.plotting import plot3d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot3d((3*x+2*y-2, (x,-5,5), (y,-5,5)),\n",
    "      (x-2*y-3, (x,-5,5), (y,-5,5)),\n",
    "      (2*x+y-1, (x,-5,5), (y,-5,5)));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As before, we can view this problem as a column picture."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Conclusion"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have seen how linear systems can be viewed as rows or columns and how they can be seen as matrices and vectors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.10.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}