L4Axb.ipynb

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     "source": [
      "$A{\\bf x} = {\\bf b}$"
     ]
    },
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     "cell_type": "code",
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     "input": [
      "%matplotlib inline\n",
      "%config InlineBackend.figure_format='retina'\n",
      "# possible questions: 35, 60, 61\n",
      "# import libraries\n",
      "import numpy as np\n",
      "import matplotlib as mp\n",
      "import pandas as pd\n",
      "import matplotlib.pyplot as plt\n",
      "import laUtilities as ut\n",
      "import slideUtilities as sl\n",
      "from IPython.display import Image\n",
      "from IPython.display import display_html\n",
      "from IPython.display import display\n",
      "reload(ut)\n",
      "print ''"
     ],
     "language": "python",
     "metadata": {
      "internals": {},
      "slideshow": {
       "slide_type": "skip"
      }
     },
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 1
    },
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     "input": [
      "%%html\n",
      "<style>\n",
      " .container.slides .celltoolbar, .container.slides .hide-in-slideshow {\n",
      "    display: None ! important;\n",
      "}\n",
      "</style>"
     ],
     "language": "python",
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       "slide_helper": "subslide_end"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "skip"
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     },
     "outputs": [
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        "<style>\n",
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        "    display: None ! important;\n",
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        "<IPython.core.display.HTML at 0x1035c67d0>"
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     "cell_type": "heading",
     "level": 2,
     "metadata": {
      "internals": {
       "slide_type": "subslide"
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      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "Multiplying a Matrix by a Vector"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {},
      "slideshow": {
       "slide_type": "-"
      }
     },
     "source": [
      "Last lecture we studied the vector equation:\n",
      "$$ x_1{\\bf a_1} + x_2{\\bf a_2} + ... + x_n{\\bf a_n} = {\\bf b}.$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
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       "slide_type": "-"
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     },
     "source": [
      "We also talked about how one can form a matrix from a set of vectors:\n",
      "$$ A = [{\\bf a_1} \\; {\\bf a_2} \\; ... \\;{\\bf a_n}].$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_number": 6
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       "slide_type": "fragment"
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     "source": [
      "In particular, if we have $n$ vectors ${\\bf a_1},{\\bf a_2}, ..., {\\bf a_n} \\in \\mathbb{R}^m,$ then A will be an $m \\times n$ matrix:\n",
      "\n",
      "$$ m\\left\\{\\begin{array}{c}\\;\\\\\\;\\\\\\;\\\\\\;\\\\\\;\\end{array}\\right.\\;\\;\\overbrace{\\left[\\begin{array}{cccc}\\begin{array}{c}\\vdots\\\\\\vdots\\\\{\\bf a_1}\\\\\\vdots\\\\\\vdots\\end{array}&\\begin{array}{c}\\vdots\\\\\\vdots\\\\{\\bf a_2}\\\\\\vdots\\\\\\vdots\\end{array}&\\dots&\\begin{array}{c}\\vdots\\\\\\vdots\\\\{\\bf a_n}\\\\\\vdots\\\\\\vdots\\end{array}\\\\\\end{array}\\right]}^{\\large n} $$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
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     "source": [
      "We're going to express a vector equation in a new way.  We are going to say that \n",
      "\n",
      "$$x_1{\\bf a_1} + x_2{\\bf a_2} + ... + x_n{\\bf a_n}$$\n",
      "\n",
      "is the same as:\n",
      "\n",
      "$$A{\\bf x}$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 8
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     "source": [
      "where $A = \\left[\\begin{array}{cccc}\\begin{array}{c}\\vdots\\\\\\vdots\\\\{\\bf a_1}\\\\\\vdots\\\\\\vdots\\end{array}&\\begin{array}{c}\\vdots\\\\\\vdots\\\\{\\bf a_2}\\\\\\vdots\\\\\\vdots\\end{array}&\\dots&\\begin{array}{c}\\vdots\\\\\\vdots\\\\{\\bf a_n}\\\\\\vdots\\\\\\vdots\\end{array}\\\\\\end{array}\\right]$ and ${\\bf x} = \\left[\\begin{array}{c}x_1\\\\x_2\\\\\\vdots\\\\x_n\\end{array}\\right].$"
     ]
    },
    {
     "cell_type": "markdown",
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       "slide_type": "fragment"
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     "source": [
      "What we have done is to define __Matrix-vector multiplication__.  That is, $A{\\bf x}$ denotes multiplying a matrix and a vector, and we define it to be the same as a linear combination of the $\\{\\bf a_1, a_2, \\dots, a_n\\}$ with weights $x_1, x_2, \\dots, x_n.$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
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       "frag_number": 10
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       "slide_type": "fragment"
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     "source": [
      "Here is the definition: \n",
      "\n",
      "If $A$ is an $m\\times n$ matrix, with columns $\\bf a_1, a_2, \\dots, a_n,$ and if ${\\bf x} \\in \\mathbb{R}^n,$ then the __product of $A$ and $\\bf x$,__ denoted $A{\\bf x}$, is __the linear combination of the columns of $A$ using the corresponding entries in $x$ as weights;__ that is,\n",
      "\n",
      "$$ A{\\bf x} = [{\\bf a_1} \\; {\\bf a_2} \\; ... \\;{\\bf a_n}]\\;\\left[\\begin{array}{c}x_1\\\\x_2\\\\\\vdots\\\\x_n\\end{array}\\right] = x_1{\\bf a_1} + x_2{\\bf a_2} + ... + x_n{\\bf a_n}.$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
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       "frag_helper": "fragment_end",
       "frag_number": 10,
       "slide_helper": "subslide_end"
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      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "-"
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     "source": [
      "Notice that if $A$ is an $m\\times n$ matrix, then ${\\bf x}$ must be in $\\mathbb{R}^n$ in order for this operation to be defined.  That is, the number of __columns__ of $A$ must match the number of __rows__ of ${\\bf x}.$\n",
      "\n",
      "If the number of columns of $A$ does not match the number of rows of ${\\bf x}$, then $A{\\bf x}$ has no meaning."
     ]
    },
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     "level": 2,
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     "source": [
      "Example."
     ]
    },
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     "cell_type": "markdown",
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       "frag_helper": "fragment_end",
       "frag_number": 10
      },
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     },
     "source": [
      "$$\\left[\\begin{array}{rrr}1&2&-1\\\\0&-5&3\\end{array}\\right]\\;\\left[\\begin{array}{r}4\\\\3\\\\7\\end{array}\\right] =$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 14
      },
      "slideshow": {
       "slide_type": "fragment"
      }
     },
     "source": [
      "$$ 4\\left[\\begin{array}{r}1\\\\0\\end{array}\\right] + 3\\left[\\begin{array}{r}2\\\\-5\\end{array}\\right] + 7\\left[\\begin{array}{r}-1\\\\3\\end{array}\\right] \n",
      "= $$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 15
      },
      "slideshow": {
       "slide_type": "fragment"
      }
     },
     "source": [
      "$$\\left[\\begin{array}{r}4\\\\0\\end{array}\\right] + \\left[\\begin{array}{r}6\\\\-15\\end{array}\\right]+ \\left[\\begin{array}{r}-7\\\\21\\end{array}\\right] = $$"
     ]
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    {
     "cell_type": "markdown",
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       "frag_number": 16,
       "slide_helper": "subslide_end"
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      "slide_helper": "slide_end",
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     "source": [
      "$$\\left[\\begin{array}{r}3\\\\6\\end{array}\\right] $$"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 16,
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     "source": [
      "Example."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
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       "frag_helper": "fragment_end",
       "frag_number": 16
      },
      "slideshow": {
       "slide_type": "-"
      }
     },
     "source": [
      "For ${\\bf v_1}, {\\bf v_2}, {\\bf v_3} \\in \\mathbb{R}^m,$ write the linear combination $3{\\bf v_1} + 5{\\bf v_2} + 7{\\bf v_3}$ as a matrix times a vector."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 19,
       "slide_helper": "subslide_end"
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      "slide_helper": "slide_end",
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       "slide_type": "fragment"
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     },
     "source": [
      "$$3{\\bf v_1} + 5{\\bf v_2} + 7{\\bf v_3} = [{\\bf v_1} \\; {\\bf v_2} \\; {\\bf v_3}]\\;\\left[\\begin{array}{c}3\\\\5\\\\7\\end{array}\\right] = A{\\bf x}.$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 19,
       "slide_type": "subslide"
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      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "Notice that if $A = [{\\bf a_1} \\; {\\bf a_2} \\; ... \\;{\\bf a_n}]$ then $A{\\bf x}$ is some point that lies in Span$\\{{\\bf a_1},{\\bf a_2}, \\dots ,{\\bf a_n}\\}$."
     ]
    },
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     "input": [
      "sl.hide_code_in_slideshow()\n",
      "ax = ut.plotSetup3d(-5,5,-7,7,-10,10)\n",
      "v = [4.0,4.0,2.0]\n",
      "u = [-4.0,3.0,1.0]\n",
      "A = np.array([v, u]).T\n",
      "x = np.array([[-0.1, -0.75]]).T\n",
      "Ax = A.dot(x)\n",
      "ax.text(v[0],v[1],v[2],r'$\\bf a_1$',size=20)\n",
      "ax.text(u[0],u[1],u[2],r'$\\bf a_2$',size=20)\n",
      "ax.text(Ax[0],Ax[1],Ax[2],r'$A\\bf x$',size=20)\n",
      "ax.text(1,-4,-10,r'Span{$\\bf a_1,a_2$}',size=16)\n",
      "ax.text(0.2,0.2,-4,r'$\\bf 0$',size=20)\n",
      "# plotting the span of v\n",
      "ut.plotSpan3d(ax,u,v,'Green')\n",
      "ut.plotPoint3d(ax,u[0],u[1],u[2],'r')\n",
      "ut.plotPoint3d(ax,v[0],v[1],v[2],'r')\n",
      "ut.plotPoint3d(ax,0,0,0,'b')\n",
      "ut.plotPoint3d(ax,Ax[0],Ax[1],Ax[2],'b')\n",
      "# plotting the axes\n",
      "ut.plotIntersection3d(ax,[0,0,1,0],[0,1,0,0])\n",
      "ut.plotIntersection3d(ax,[0,0,1,0],[1,0,0,0])\n",
      "ut.plotIntersection3d(ax,[0,1,0,0],[1,0,0,0])\n",
      "ax.set_title(r'$A{\\bf x}$ where $A = \\left[\\bf a_1\\;a_2\\right]$',size=20)\n",
      "print ''"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 19,
       "slide_helper": "subslide_end"
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      "slide_helper": "slide_end",
      "slideshow": {
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     "outputs": [
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kg+CGw2EEAoGyRJr0+bUEYQWlCHCpbZA5+vH04tubFAh9ww2CIJyHRJcgXEAu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\nvfIQqekj6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tJWWCfL9hBuyp1MtzcUm0K8xJKmEK/vOhbxm5OXg7/OmoBXJtwFn+czADdI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       "text": [
        "<matplotlib.figure.Figure at 0x10df1eb90>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 19,
       "slide_helper": "subslide_end",
       "slide_type": "subslide"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "Question Time! Q4.1"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 19,
       "slide_type": "subslide"
      },
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "The Matrix Equation"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 19
      },
      "slideshow": {
       "slide_type": "-"
      }
     },
     "source": [
      "Now let's write an equation.   Let's start with a linear system:\n",
      "\n",
      "$$\\begin{array}{rcl}x_1+2x_2-x_3&=&4\\\\-5x_2+3x_3&=&1\\end{array}$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 25
      },
      "slideshow": {
       "slide_type": "fragment"
      }
     },
     "source": [
      "We saw last lecture that this linear system is equivalent to a vector equation, namely\n",
      "\n",
      "$$x_1\\left[\\begin{array}{r}1\\\\0\\end{array}\\right] + x_2\\left[\\begin{array}{r}2\\\\-5\\end{array}\\right] + x_3\\left[\\begin{array}{r}-1\\\\3\\end{array}\\right] = \\left[\\begin{array}{r}4\\\\1\\end{array}\\right]$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 26
      },
      "slideshow": {
       "slide_type": "fragment"
      }
     },
     "source": [
      "Now, today we have learned that this vector equation is also equivalent to this __matrix equation__:\n",
      "\n",
      "$$\\left[\\begin{array}{rrr}1&2&-1\\\\0&-5&3\\end{array}\\right]\\;\\left[\\begin{array}{r}x_1\\\\x_2\\\\x_3\\end{array}\\right] = \\left[\\begin{array}{r}4\\\\1\\end{array}\\right].$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 27
      },
      "slideshow": {
       "slide_type": "fragment"
      }
     },
     "source": [
      "which has the form $A{\\bf x} = {\\bf b}$.  "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 28,
       "slide_helper": "subslide_end"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "fragment"
      }
     },
     "source": [
      "Notice how simple it is to go from the linear system to the matrix equation: we put the coefficients of the linear system into $A$, and the right hand side values into ${\\bf b},$ and we can then write the matrix equation $A{\\bf x} = {\\bf b}$ immediately."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 28,
       "slide_type": "subslide"
      },
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "OK, let's write this out formally.\n",
      "\n",
      "__Theorem.__  If $A$ is an $m\\times n$ matrix, with columns $\\bf a_1, a_2, \\dots, a_n,$ and if $\\bf b$ is in $\\mathbb{R}^m$, the matrix equation\n",
      "\n",
      "$$ A{\\bf x} = {\\bf b}$$\n",
      "\n",
      "has the same solution set as the vector equation\n",
      "\n",
      "$$ x_1{\\bf a_1} + x_2{\\bf a_2} + ... + x_n{\\bf a_n} = {\\bf b}$$\n",
      "\n",
      "which, in turn, has the same solution set as the system of linear equations whose augmented matrix is\n",
      "\n",
      "$$[{\\bf a_1} \\; {\\bf a_2} \\; ... \\;{\\bf a_n}\\;{\\bf b}].$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 30
      },
      "slideshow": {
       "slide_type": "fragment"
      }
     },
     "source": [
      "This is an absolutely key result, because it gives us power to solve problems from three different viewpoints.  If we are looking for a solution set $x_1, x_2, \\dots, x_n,$ there are three different questions we can ask:\n",
      "\n",
      "1. What is the solution set of the linear system $[{\\bf a_1} \\; {\\bf a_2} \\; ... \\;{\\bf a_n}\\;{\\bf b}]$?\n",
      "2. What is the solution set of the vector equation $x_1{\\bf a_1} + x_2{\\bf a_2} + ... + x_n{\\bf a_n} = {\\bf b}?$\n",
      "3. What is the solution set of the matrix equation $A{\\bf x} = {\\bf b}?$\n",
      "\n",
      "We now know that all these questions have the same answer.  And all of them can be solved by row reducing the augmented matrix $[{\\bf a_1} \\; {\\bf a_2} \\; ... \\;{\\bf a_n}\\;{\\bf b}].$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 31,
       "slide_helper": "subslide_end"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "fragment"
      }
     },
     "source": [
      "In particular, one of the most common questions you will encounter is, given a matrix $A$ and a vector ${\\bf b}$, is there an ${\\bf x}$ that makes $A{\\bf x} = {\\bf b}$ true?\n",
      "\n",
      "You will encounter this form of question quite often in fields like computer graphics, data mining, algorithms, or quantum computing."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 31,
       "slide_helper": "subslide_end",
       "slide_type": "subslide"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "Question Time! Q4.2"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 31,
       "slide_type": "subslide"
      },
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "Existence of Solutions"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 31
      },
      "slideshow": {
       "slide_type": "-"
      }
     },
     "source": [
      "We can see that $A{\\bf x} = {\\bf b}$ has a solution if and only if $\\bf b$ is a linear combination of the columns of $A$ -- that is, if $\\bf b$ lies in Span$\\{{\\bf a_1},{\\bf a_2}, \\dots ,{\\bf a_n}\\}.$   We can adopt the term \"consistent\" here too -- i.e., is $A{\\bf x} = {\\bf b}$ consistent?"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 35
      },
      "slideshow": {
       "slide_type": "fragment"
      }
     },
     "source": [
      "Now we will ask a more general question, which is specifically about the matrix $A$.  That is:\n",
      "\n",
      "Does $A{\\bf x} = {\\bf b}$ have a solution for _any_ ${\\bf b}$?"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 36
      },
      "slideshow": {
       "slide_type": "fragment"
      }
     },
     "source": [
      "__Example.__ \n",
      "\n",
      "Let $A = \\left[\\begin{array}{rrr}1&3&4\\\\-4&2&-6\\\\-3&-2&-7\\end{array}\\right]$ and ${\\bf b} = \\left[\\begin{array}{r}b_1\\\\b_2\\\\b_3\\end{array}\\right].$  Is the equation $A{\\bf x} = {\\bf b}$ consistent for all possible $b_1, b_2, b_3?$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 37
      },
      "slideshow": {
       "slide_type": "fragment"
      }
     },
     "source": [
      "We know how to test for consistency: form the augmented matrix and row reduce it.\n",
      "\n",
      "$$\\left[\\begin{array}{rrrc}1&3&4&b_1\\\\-4&2&-6&b_2\\\\-3&-2&-7&b_3\\end{array}\\right] \\sim \\left[\\begin{array}{rrrc}1&3&4&b_1\\\\0&14&10&b_2+4b_1\\\\0&7&5&b_3+3b_1\\end{array}\\right] \\sim \\left[\\begin{array}{rrrc}1&3&4&b_1\\\\0&14&10&b_2+4b_1\\\\0&0&0&b_3+3b_1-\\frac{1}{2}(b_2 + 4b_1)\\end{array}\\right].$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 38
      },
      "slideshow": {
       "slide_type": "fragment"
      }
     },
     "source": [
      "The third entry in the column 4, simplified, is $b_1 -\\frac{1}{2}b_2+ b_3.$ This expression can be nonzero. \n",
      "\n",
      "For example, take $b_1 = 1, b_2 = 1, b_3 = 1;$ then the lower right entry is 1.5.  This gives a row of the form $0 = k$ which indicates an inconsistent system.  \n",
      "\n",
      "So the answer is \"no, $A{\\bf x} = {\\bf b}$ is __not__ consistent for all possible $b_1, b_2, b_3.$\""
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 39,
       "slide_helper": "subslide_end"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "fragment"
      }
     },
     "source": [
      "\n",
      "\n",
      "Here is the echelon form of $A$ (note we are talking only about $A$ here, not the augmented matrix):\n",
      "\n",
      "$$\\left[\\begin{array}{rrr}1&3&4\\\\0&14&10\\\\0&0&0\\end{array}\\right].$$\n",
      "\n",
      "The equation $A{\\bf x} = {\\bf b}$ fails to be consistent for all $\\bf b$ because the echelon form of $A$ has a row of zeros.  \n",
      "\n",
      "If $A$ had a pivot in all three rows, we would not care about the calculations in the augmented column because no matter what is in the augmented column, an echelon form of the augmented matrix could not have a row indicating $0 = k$."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 39,
       "slide_type": "subslide"
      },
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "_Question:_ OK, so $A{\\bf x} = {\\bf b}$ is not always consistent.  When __is__ $A{\\bf x} = {\\bf b}$ consistent?"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 41
      },
      "slideshow": {
       "slide_type": "fragment"
      }
     },
     "source": [
      "_Answer:_ When $b_1 -\\frac{1}{2}b_2+ b_3 = 0.$  This makes the last row of the augmented matrix all zeros.\n",
      "\n",
      "This is a single equation in three unknowns, so it defines a plane through the origin in $\\mathbb{R}^3.$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sl.hide_code_in_slideshow()\n",
      "# %matplotlib qt\n",
      "ax = ut.plotSetup3d(-5,5,-7,7,-10,10)\n",
      "a1 = [1.0,-4.0,-3.0]\n",
      "a2 = [3.0,2.0,-2.0]\n",
      "a3 = [4.0, -6.0, -7]\n",
      "ax.text(a1[0],a1[1],a1[2],r'$\\bf a_1$',size=20)\n",
      "ax.text(a2[0],a2[1],a2[2],r'$\\bf a_2$',size=20)\n",
      "ax.text(a3[0],a3[1],a3[2],r'$\\bf a_3$',size=20)\n",
      "#ax.text(1,-4,-10,r'Span{$\\bf a_1,a_2,a_3$}',size=16)\n",
      "ax.text(0.2,0.2,-4,r'$\\bf 0$',size=20)\n",
      "# plotting the span of v\n",
      "ut.plotSpan3d(ax,a1,a2,'Green')\n",
      "ut.plotPoint3d(ax,a1[0],a1[1],a1[2],'r')\n",
      "ut.plotPoint3d(ax,a2[0],a2[1],a2[2],'r')\n",
      "ut.plotPoint3d(ax,a3[0],a3[1],a3[2],'r')\n",
      "ut.plotPoint3d(ax,0,0,0,'b')\n",
      "# plotting the axes\n",
      "#ut.plotIntersection3d(ax,[0,0,1,0],[0,1,0,0])\n",
      "#ut.plotIntersection3d(ax,[0,0,1,0],[1,0,0,0])\n",
      "#ut.plotIntersection3d(ax,[0,1,0,0],[1,0,0,0])\n",
      "ax.set_title(r'$b_1 - \\frac{1}{2}b_2 + b_3 = 0$',size=20)\n",
      "# ax.mouse_init()\n",
      "print ''"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 42
      },
      "slideshow": {
       "slide_type": "fragment"
      }
     },
     "outputs": [
      {
       "html": [
        "<div id=\"c09ca56b15cd458a\"></div>\n",
        "    <script type=\"text/javascript\">\n",
        "        $(function(){\n",
        "            var p = $(\"#c09ca56b15cd458a\");\n",
        "            if (p.length==0) return;\n",
        "\n",
        "            while (!p.hasClass(\"cell\")) {\n",
        "                p=p.parent();\n",
        "\n",
        "                if (p.prop(\"tagName\") ==\"body\") return;\n",
        "            }\n",
        "            var cell = p;\n",
        "            cell.find(\".input\").addClass(\"hide-in-slideshow\")\n",
        "        });\n",
        "    </script>"
       ],
       "metadata": {},
       "output_type": "display_data"
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
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      {
       "metadata": {
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         "width": 349
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       },
       "output_type": "display_data",
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g7IZElyCKpFLBjUQi8Pv9i4rTW0mxjRwq5VjsGPaf3I9AMIAgvCu6GpIi4bWZ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\nrG1aa+NeEm7Byx/szcDtEV2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md9HUBNiYeudU97d8uDmiG4vFAACtra0Oz6Q6ING1gUQi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XDJxb9cu7Biya8gCiUtuUuShBSfaRdml560mpDzPRBFCKKQocvXulMY34NqqlZmsyZTHR+ILKcI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\nRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10df46290>"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 43
      },
      "slideshow": {
       "slide_type": "fragment"
      }
     },
     "source": [
      "The set of points that makes $b_1 - \\frac{1}{2}b_2 + b_3 = 0$ is the set of $\\bf b$ values that makes $A{\\bf x} = {\\bf b}$ consistent.  But if $A{\\bf x} = {\\bf b}$ then ${\\bf b}$ lies within Span$\\{\\bf a_1, a_2, a_3\\}$.  "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 44
      },
      "slideshow": {
       "slide_type": "fragment"
      }
     },
     "source": [
      "So we have determined that Span$\\{\\bf a_1, a_2, a_3\\}$ is the same point set as $b_1 - \\frac{1}{2}b_2 + b_3 = 0$.\n",
      "\n",
      "That means that Span$\\{\\bf a_1, a_2, a_3\\}$ is a _plane_ in this case.  In the figure we have plotted $\\bf a_1, a_2,$ and $\\bf a_3$ and you can see that all three points, as well as the origin, lie in the same plane."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 45,
       "slide_helper": "subslide_end"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "fragment"
      }
     },
     "source": [
      "Now, in the most general case, four points will _not_ line in a plane.  In other words, the span of three vectors in $\\mathbb{R}^3$ can be the whole space $\\mathbb{R}^3$."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 45,
       "slide_helper": "subslide_end",
       "slide_type": "subslide"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "Question Time! Q4.3"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 45,
       "slide_type": "subslide"
      },
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "Now we will tie together all three views of our question.\n",
      "\n",
      "__Theorem:__ Let $A$ be an $m \\times n$ matrix.  Then the following statements are logically equivalent.  That is, for a particular $A,$ either they are all true or they are all false.\n",
      "\n",
      "1. For each $\\bf b$ in $\\mathbb{R}^n,$ the equation $A{\\bf x} = {\\bf b}$ has a solution.\n",
      "1. Each $\\bf b$ in $\\mathbb{R}^n$ is a linear combination of the columns of $A$.\n",
      "1. The columns of $A$ span $\\mathbb{R}^m$.\n",
      "1. $A$ has a pivot position in every row."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 48,
       "slide_helper": "subslide_end"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "fragment"
      }
     },
     "source": [
      "This theorem is very powerful and general.  Notice that we started by thinking about a matrix equation, but we ended by making statements about $A$ alone.  This is the first time we are studying the property of a matrix itself; we will study many properties of matrices on their own as we progress."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 48,
       "slide_type": "subslide"
      },
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "Inner Product"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 48
      },
      "slideshow": {
       "slide_type": "-"
      }
     },
     "source": [
      "There is a simpler way to compute the matrix-vector product.  It uses a concept called the __inner product__ or __dot product.__\n",
      "\n",
      "The inner product is defined for two sequences of numbers, and returns a single number.   For example, the expression\n",
      "\n",
      "$$[3\\;5\\;1] \\left[\\begin{array}{c}2\\\\-1\\\\4\\end{array}\\right]$$\n",
      "\n",
      "is the same as\n",
      "\n",
      "$$(3\\cdot 2) + (5\\cdot -1) + (1 \\cdot 4)$$\n",
      "\n",
      "which is the sum of the products of the corresponding entries, and yields the scalar value 5.  This is the inner product of the two sequences."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 51,
       "slide_helper": "subslide_end"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "fragment"
      }
     },
     "source": [
      "The general definition of the inner product is:\n",
      "\n",
      "$$[x_1\\;x_2\\;\\dots\\;x_n] \\left[\\begin{array}{c}y_1\\\\y_2\\\\\\vdots\\\\y_n\\end{array}\\right] = \\sum_{i=1}^n x_i y_i$$\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 51,
       "slide_type": "subslide"
      },
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "Let's see how this can be used to think about matrix-vector multiplication.\n",
      "\n",
      "Consider the matrix-vector multiplication\n",
      "\n",
      "$$\\left[\\begin{array}{rrr}2&3&4\\\\-1&5&-3\\\\6&-2&8\\end{array}\\right]\\;\\left[\\begin{array}{r}x_1\\\\x_2\\\\x_3\\end{array}\\right]$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 53
      },
      "slideshow": {
       "slide_type": "fragment"
      }
     },
     "source": [
      "\n",
      "$$= x_1\\left[\\begin{array}{r}2\\\\-1\\\\6\\end{array}\\right] + x_2\\left[\\begin{array}{r}3\\\\5\\\\-2\\end{array}\\right] + x_3\\left[\\begin{array}{r}4\\\\-3\\\\8\\end{array}\\right]$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 54
      },
      "slideshow": {
       "slide_type": "fragment"
      }
     },
     "source": [
      "\n",
      "$$= \\left[\\begin{array}{r}2x_1\\\\-1x_1\\\\6x_1\\end{array}\\right] + \\left[\\begin{array}{r}3x_2\\\\5x_2\\\\-2x_2\\end{array}\\right] + \\left[\\begin{array}{r}4x_3\\\\-3x_3\\\\8x_3\\end{array}\\right]$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 55
      },
      "slideshow": {
       "slide_type": "fragment"
      }
     },
     "source": [
      "\n",
      "$$= \\left[\\begin{array}{r}2x_1+3x_2+4x_3\\\\-1x_1+5x_2-3x_3\\\\6x_1-2x_2+8x_3\\end{array}\\right] $$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 56,
       "slide_helper": "subslide_end"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "fragment"
      }
     },
     "source": [
      "Now, what is the first entry in the result?  It is the _inner product_ of the first row of $A$ and $\\bf x$.  That is, \n",
      "\n",
      "$$[2\\;3\\;4] \\left[\\begin{array}{c}x_1\\\\x_2\\\\x_3\\end{array}\\right] = [2x_1+3x_2+4x_3]$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 56,
       "slide_type": "subslide"
      },
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "This is a fast and simple way to compute the result of a matrix-vector product.  Each element of the result is the _inner product_ of the corresponding row of $A$ and the vector $\\bf x$."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 58,
       "slide_helper": "subslide_end"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "fragment"
      }
     },
     "source": [
      "$$ \\left[\\begin{array}{ccc}2&3&4\\\\&&\\\\&&\\end{array}\\right]\\left[\\begin{array}{c}x_1\\\\x_2\\\\x_3\\end{array}\\right] = \\left[\\begin{array}{ccc}2x_1&+3x_2&+4x_3\\\\&&\\\\&&\\end{array}\\right]$$\n",
      "\n",
      "$$ \\left[\\begin{array}{ccc}&&\\\\-1&5&-3\\\\&&\\end{array}\\right]\\left[\\begin{array}{c}x_1\\\\x_2\\\\x_3\\end{array}\\right] = \\left[\\begin{array}{ccc}&&\\\\-x_1&+5x_2&-3x_3\\\\&&\\end{array}\\right]$$"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 58,
       "slide_type": "subslide"
      },
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "Example."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 58,
       "slide_helper": "subslide_end"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "-"
      }
     },
     "source": [
      "$$\\left[\\begin{array}{rrr}1&2&-1\\\\0&-5&3\\end{array}\\right]\\left[\\begin{array}{r}4\\\\3\\\\7\\end{array}\\right] = \\left[\\begin{array}{rrr}1\\cdot 4&+2\\cdot 3&-1\\cdot 7\\\\0\\cdot 4&-5\\cdot 3&+3\\cdot 7\\end{array}\\right] = \\left[\\begin{array}{r}3\\\\6\\end{array}\\right].$$"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 58,
       "slide_type": "subslide"
      },
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "An (I)nteresting matrix"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 58
      },
      "slideshow": {
       "slide_type": "-"
      }
     },
     "source": [
      "Consider this matrix equation:\n",
      "\n",
      "$$\\left[\\begin{array}{rrr}1&0&0\\\\0&1&0\\\\0&0&1\\end{array}\\right]\\;\\left[\\begin{array}{r}r\\\\s\\\\t\\end{array}\\right] = \\left[\\begin{array}{rrr}1\\cdot r&+0\\cdot s&+0\\cdot t\\\\0\\cdot r&+1\\cdot s&+0\\cdot t\\\\0\\cdot r&+0\\cdot s&+1\\cdot t\\end{array}\\right] = \\left[\\begin{array}{r}r\\\\s\\\\t\\end{array}\\right].$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 63,
       "slide_helper": "subslide_end"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "fragment"
      }
     },
     "source": [
      "This sort of matrix -- with 1s on the diagonal and 0s everywhere else -- is called an __identity matrix__ and is denoted by $I$.\n",
      "\n",
      "You can see that for any $\\bf x$, $I\\bf x = x.$"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 63,
       "slide_type": "subslide"
      },
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "Algebraic Properties of the Matrix-Vector Product"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 63
      },
      "slideshow": {
       "slide_type": "-"
      }
     },
     "source": [
      "__Theorem.__ If $A$ is an $m \\times n$ matrix, $\\bf u$ and $\\bf v$ are vectors in $\\mathbb{R}^n$, and $c$ is a scalar, then:\n",
      "\n",
      "1. $A({\\bf u} + {\\bf v}) = A{\\bf u} + A{\\bf v};$\n",
      "1. $A(c{\\bf u}) = c(A{\\bf u}).$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 66
      },
      "slideshow": {
       "slide_type": "fragment"
      }
     },
     "source": [
      "__Proof:__ Let us take $n=3$, $A = [\\bf a_1\\;a_2\\;a_3],$ and $\\bf u,v \\in \\mathbb{R}^3.$  \n",
      "\n",
      "Then to prove (1.):\n",
      "\n",
      "$$A({\\bf u} + {\\bf v}) = [{\\bf a_1\\;a_2\\;a_3}]\\left[\\begin{array}{r}u_1+v_1\\\\u_2+v_2\\\\u_3+v_3\\end{array}\\right]$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 67
      },
      "slideshow": {
       "slide_type": "fragment"
      }
     },
     "source": [
      "\n",
      "$$=(u_1+v_1){\\bf a_1} + (u_2+v_2){\\bf a_2} + (u_3+v_3){\\bf a_3}$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 68
      },
      "slideshow": {
       "slide_type": "fragment"
      }
     },
     "source": [
      "\n",
      "$$=(u_1{\\bf a_1} + u_2{\\bf a_2} + u_3{\\bf a_3}) + (v_1{\\bf a_1} + v_2{\\bf a_2} + v_3{\\bf a_3})$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 69
      },
      "slideshow": {
       "slide_type": "fragment"
      }
     },
     "source": [
      "\n",
      "$$=A{\\bf u} + A{\\bf v}.$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 70
      },
      "slideshow": {
       "slide_type": "fragment"
      }
     },
     "source": [
      "And to prove (2.):\n",
      "\n",
      "$$A(c{\\bf u}) = [{\\bf a_1\\;a_2\\;a_3}]\\left[\\begin{array}{r}c u_1\\\\c u_2\\\\c u_3\\end{array}\\right]$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 71
      },
      "slideshow": {
       "slide_type": "fragment"
      }
     },
     "source": [
      "$$ = (c u_1){\\bf a_1} + (c u_2){\\bf a_2} + (c u_3){\\bf a_3}$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 72
      },
      "slideshow": {
       "slide_type": "fragment"
      }
     },
     "source": [
      "$$= c (u_1{\\bf a_1}) + c (u_2{\\bf a_2}) + c (u_3{\\bf a_3})$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 73
      },
      "slideshow": {
       "slide_type": "fragment"
      }
     },
     "source": [
      "$$= c (u_1{\\bf a_1} + u_2{\\bf a_2} + u_3{\\bf a_3})$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 74,
       "slide_helper": "subslide_end"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "fragment"
      }
     },
     "source": [
      "$$= c (A{\\bf u}).$$"
     ]
    }
   ],
   "metadata": {}
  }
 ]
}