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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## CS 132 Homework 03 B  Solution -- \n",
    "\n",
    "### Due Wednesday July 28th at Midnight (1 minute after 11:59pm) in Gradescope (with grace period of 6 hours)\n",
    "### Homeworks may be submitted up to 24 hours late with a 10% penalty (same grace period)\n",
    "\n",
    "\n",
    "Please read through the entire notebook, reading the expository material and then do the problems, following the instuctions to try various features; among the exposition of various features of Python there\n",
    "are three problems which will be graded.  The homework is worth 30 points. \n",
    "\n",
    "You will need to complete this notebook and then convert to a PDF file in order to submit to Gradescope. Instructions are given here:\n",
    "\n",
    "https://www.cs.bu.edu/fac/snyder/cs132/HWSubmissionInstructions.html\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Here are some imports which will be used in the code in the rest of the lab  \n",
    "\n",
    "# Imports used for the code in CS 237\n",
    "\n",
    "import numpy as np                # arrays and functions which operate on arrays\n",
    "\n",
    "import matplotlib.pyplot as plt   # normal plotting\n",
    "\n",
    "\n",
    "# NOTE: You may not use any other libraries than those listed here without explicit permission."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Gaussian Elimination\n",
    "\n",
    "# number of digits of precision to print out\n",
    "\n",
    "prec = 4\n",
    "\n",
    "########################################################################################################\n",
    "\n",
    "# Returns the Row Echelon (upper triangular) form\n",
    "\n",
    "def forwardElimination(A,traceLevel=0):\n",
    "    \n",
    "    A = (np.copy(A)).astype(float)\n",
    "    \n",
    "    if (traceLevel > 0):\n",
    "        print(\"\\nRunning Forward Elimination on:\\n\")\n",
    "        print(np.round(A, decimals=4),\"\\n\")\n",
    "        print()\n",
    "    \n",
    "    (numRows,numCols) = A.shape\n",
    "    \n",
    "    # r = row we are currently working on         pivot value is A[r][c]\n",
    "    r = 0            \n",
    "    for c in range(numCols):     # solve for variable in column c \n",
    "        # find row in column c with first non-zero element, and exchange with row r                  \n",
    "        r1 = r\n",
    "        while(r1 < numRows):\n",
    "            if (not np.isclose(A[r1][c],0.0)):   # A[r1][c] is first non-zero element at or below r in column c\n",
    "                break\n",
    "            r1 += 1\n",
    "        \n",
    "        if(r1 == numRows):    # all zeros below r in this column\n",
    "            continue          # go on to the next column, but still working on same row   \n",
    "         \n",
    "        if(r1 != r): \n",
    "            # exchange rows r1 and r\n",
    "            A[[r1,r],:] = A[[r,r1],:] \n",
    "            if (traceLevel == 2): \n",
    "                print(\"Exchange R\" + str(r1+1) + \" and R\" + str(r+1) + \"\\n\") \n",
    "                print(np.round(A, decimals=4))                \n",
    "                print() \n",
    "\n",
    "        # now use pivot A[r][c] to eliminate all vars in this column below row r\n",
    "        for r2 in range(r+1,numRows):\n",
    "            rowReduce(A,r,c,r2,traceLevel)\n",
    "            \n",
    "        r += 1  \n",
    "        if (r >= numRows):\n",
    "            break\n",
    "            \n",
    "    return A\n",
    "\n",
    "# for pivot A[r][c], eliminate variable in location A[r2][c] in row r2 using row operations\n",
    "\n",
    "def rowReduce(A,r,c,r2,traceLevel=0):\n",
    "\n",
    "    if(not np.isclose(A[r2][c],0.0)):\n",
    "\n",
    "        factor = -A[r2][c]/A[r][c] \n",
    "        A[r2] += factor * A[r]\n",
    "            \n",
    "        if(traceLevel == 2):\n",
    "            print(\"R\" + str(r2+1) + \" += \" + str(np.around(factor,prec)) + \"*R\" + str(r+1) + \"\\n\")  \n",
    "            print(np.round(A, decimals=4))\n",
    "            print()\n",
    "\n",
    "# Take a Row Echelon Form and return a Reduced Row Echelon Form\n",
    "\n",
    "def backwardSubstitute(A,augmented=True,traceLevel=0): \n",
    "    \n",
    "    numRows,numCols = A.shape\n",
    "    \n",
    "    if (A.dtype != 'float64'):\n",
    "        A = A.astype(float)\n",
    "\n",
    "    # now back-substitute the variables from bottom row to top\n",
    "    if (traceLevel > 0):\n",
    "        print(\"Creating Reduced Row Echelon Form...\\n\") \n",
    "\n",
    "    for r in range(numRows):\n",
    "\n",
    "        # find variable in this row\n",
    "        for c in range(numCols):\n",
    "            if(not np.isclose(A[r][c],0.0)):\n",
    "                break \n",
    "       \n",
    "        if ((augmented and c >= numCols-1) or (c >= numCols)):        # inconsistent or redundant row\n",
    "                continue \n",
    "                        \n",
    "        # A[r][c] is variable to eliminate\n",
    "        \n",
    "        factor = A[r][c]\n",
    "        \n",
    "        if (np.isclose(factor,0.0)):   # already eliminated\n",
    "            continue\n",
    "        \n",
    "        if(not np.isclose(factor,1.0)):  \n",
    "            A[r] *= 1/factor\n",
    "            if (traceLevel == 2):\n",
    "                print(\"R\" + str(r+1) + \" = R\" + str(r+1) + \"/\" + str(np.around(factor,prec)) + \"\\n\")  \n",
    "                print(np.round(A, decimals=4))\n",
    "                print()\n",
    "\n",
    "        for r2 in range(r): \n",
    "            rowReduce(A,r,c,r2,traceLevel)\n",
    "            \n",
    "    return A \n",
    "\n",
    "    \n",
    "# try to find row of all zeros except for last column, in augmented matrix. \n",
    "\n",
    "def noSolution(A):\n",
    "    numRows,numCols = A.shape\n",
    "    for r in range(numRows-1,-1,-1):         # start from bottom, since inconsistent rows end up there\n",
    "        for c in range(numCols):\n",
    "            if(not np.isclose(A[r][c],0.0)):  # found first non-0 in this row\n",
    "                if(c == numCols-1):\n",
    "                    return True\n",
    "                else:\n",
    "                    break\n",
    "    return False\n",
    "\n",
    "########################################################################################################\n",
    "\n",
    "# Runs GE and returns a reduced row echelon form\n",
    "\n",
    "# If b == None assumes that A is NOT an augmented matrix, and runs GE and returns Reduced Row Echelon Form\n",
    "\n",
    "# If b is a column matrix then adjoins it to A and runs GE;\n",
    "#       Always returns the Reduced Row Echelon Form\n",
    "#       If inconsistent then also prints out \"Inconsistent!\"\n",
    "\n",
    "# If b is a length n array instead of a 1 x n array (column vector)\n",
    "# b will be converted to a column vector, for convenience. \n",
    "\n",
    "# traceLevel 0 will not print anything out during the run\n",
    "# traceLevel 1 will print out various stages of the process and the intermediate matrices\n",
    "# traceLevel 2 will also print out the row operations used at each step. \n",
    "\n",
    "# If you want to produce an Echelon Form (NOT reduced), then use forwardElimination instead. \n",
    "\n",
    "# See examples for more explanation of how to use this\n",
    "\n",
    "def GaussianElimination(A,b=None, traceLevel = 0):\n",
    "    if( type(b) != type(None)):\n",
    "        if( (A.shape)[0] == 1 ):\n",
    "            b = np.array([b]).T\n",
    "        Ab = (np.hstack((A.copy(),b))).astype(float)\n",
    "    else:\n",
    "        Ab = A.copy().astype(float)\n",
    "        \n",
    "    if( traceLevel > 0 and type(b) == type(None)):\n",
    "        print(\"\\nCreating Reduced Row Echelon Form:\\n\")\n",
    "        print(np.round(Ab, decimals=4))\n",
    "    elif( traceLevel > 0 ):\n",
    "        print(\"\\nRunning Gaussian Elimination on augmented matrix:\\n\")\n",
    "        print(np.round(Ab, decimals=4))\n",
    "    \n",
    "    B = forwardElimination(Ab,traceLevel)\n",
    "    \n",
    "    if( traceLevel > 0 ):\n",
    "        print(\"\\nEchelon Form:\\n\")\n",
    "        print( np.round(B, decimals=4) + np.zeros(B.shape),\"\\n\")       # adding -0.0 + 0 gives 0.0\n",
    "    \n",
    "    if ( type(b) != type(None) and noSolution(B) ):\n",
    "        print(\"No solution!\")\n",
    "\n",
    "    C = backwardSubstitute(B,type(b)!=type(None),traceLevel)\n",
    "        \n",
    "    if( traceLevel > 0 ):\n",
    "        print(\"Reduced Row Echelon Form:\\n\")\n",
    "        print( np.round(C, decimals=4) + np.zeros(C.shape),\"\\n\")   # adding -0.0 + 0 gives 0.0\n",
    "            \n",
    "    return C\n",
    "\n",
    "########################################################################################################\n",
    "  \n"
   ]
  },
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"
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem 5\n",
    "\n",
    "(A) Consider the following vectors, the last one of which has an unknown value $h$:\n",
    "\n",
    "\n",
    "![Screen%20Shot%202021-07-23%20at%203.12.04%20PM.png](attachment:Screen%20Shot%202021-07-23%20at%203.12.04%20PM.png)\n",
    "\n",
    "For what values of $h$ is the set of vectors *linearly dependent*?\n",
    "\n",
    "(B) Again, for this set of vectors:\n",
    "\n",
    "![Screen%20Shot%202021-07-23%20at%203.12.31%20PM.png](attachment:Screen%20Shot%202021-07-23%20at%203.12.31%20PM.png)\n",
    "\n",
    "\n",
    "for what values of $h$ is the set of vectors *linearly dependent*?\n",
    "\n",
    "(C)  Consider a $2\\times 2$ matrix with linearly dependent columns. List all the possible echelon forms of this\n",
    "matrix, using $\\blacksquare$ for a pivot, $0$ for a zero, and $\\ast$ for any real value.\n",
    "\n",
    "(D) Consider a $2\\times 3$ matrix whose column space is all of $\\mathbb{R}^2$. List all the possible echelon forms of this\n",
    "matrix, using $\\blacksquare$ for a pivot, $0$ for a zero, and $\\ast$ for any real value.\n",
    "\n",
    "(E) Consider a $4\\times 3$ matrix $A$ whose columns are linearly independent.  List all the possible echelon forms of this matrix, using $\\blacksquare$ for a pivot, $0$ for a zero, and $\\ast$ for any real value.\n",
    "\n",
    "\n"
   ]
  },
  {
   "attachments": {
    "Screen%20Shot%202021-07-23%20at%203.12.37%20PM.png": {
     "image/png": 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"
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Solution:**\n",
    "\n",
    "(A) all h\n",
    "\n",
    "(B) h = 26\n",
    "\n",
    "(C)\n",
    "\n",
    "![Screen%20Shot%202021-07-23%20at%203.12.37%20PM.png](attachment:Screen%20Shot%202021-07-23%20at%203.12.37%20PM.png)\n",
    "\n",
    "(D)\n",
    "$$ \\begin{bmatrix} \\blacksquare & 0 & \\ast \\\\ \n",
    "                    0 & \\blacksquare & \\ast \\\\ \\end{bmatrix} $$\n",
    "                 \n",
    "$$\\begin{bmatrix} \\blacksquare & \\ast& 0  \\\\ 0 & \\ast& \\blacksquare \\end{bmatrix} $$\n",
    "\n",
    "$$\\begin{bmatrix} 0 & \\blacksquare & 0 \\\\ 0 & 0 & \\blacksquare \\end{bmatrix}$$\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "(E)\n",
    "\n",
    "![Screen%20Shot%202021-07-23%20at%203.12.43%20PM.png](attachment:Screen%20Shot%202021-07-23%20at%203.12.43%20PM.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem 6\n",
    "\n",
    "(A)  Show that $T$ is a linear transformation by finding a matrix that implements the mapping\n",
    "\n",
    "$$T\\left (\\begin{bmatrix} x_1 \\\\  x_2 \\\\ \\end{bmatrix} \\right ) = \n",
    "\\begin{bmatrix} 2x_2 - 3x_1 \\\\ x_1 - 4x_2 \\\\ 0 \\\\ x_2\\end{bmatrix} $$\n",
    "\n",
    "(B)  Show that $T'$ is a linear transformation by finding a matrix that implements the mapping\n",
    "\n",
    "$$T'\\left (\\begin{bmatrix} x_1 \\\\  x_2 \\\\ x_3 \\\\  x_4 \\\\ \\end{bmatrix} \\right ) = \n",
    "\\begin{bmatrix} 2x_1 + 3x_3 - 4x_4 \\end{bmatrix} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Solution:**\n",
    "\n",
    "(A)  Again, we apply the transformation to the columns of $I_2$:\n",
    "\n",
    "$$ T\\left ( \\begin{bmatrix} 1 \\\\ 0 \\end{bmatrix}\\right )\\ =\\ \n",
    "\\begin{bmatrix} 2\\cdot 0 - 3\\cdot 1 \\\\ 1 - 4\\cdot 0 \\\\ 0\\\\ 0 \\end{bmatrix}\\ =\\ \\begin{bmatrix} -3  \\\\  1 \\\\ 0  \\\\ 0 \\\\\\end{bmatrix}$$\n",
    "\n",
    "$$ T\\left ( \\begin{bmatrix} 0 \\\\ 1 \\end{bmatrix}\\right )\\ =\\ \n",
    "\\begin{bmatrix} 2\\cdot 1 - 3\\cdot 0 \\\\ 0 - 4\\cdot 1 \\\\ 0\\\\ 1 \\end{bmatrix}\\ =\\ \\begin{bmatrix} 2 \\\\  -4 \\\\  0 \\\\ 1 \\\\\\end{bmatrix}$$\n",
    "\n",
    "yielding:\n",
    "\n",
    "$$\\begin{bmatrix} -3 & 2 \\\\  1 & -4 \\\\ 0 & 0 \\\\ 0 & 1 \\\\\\end{bmatrix}$$\n",
    "\n",
    "\n",
    "(B)\n",
    "\n",
    "$$ T\\left ( \\begin{bmatrix} 1 \\\\ 0 \\\\ 0 \\\\ 0\\end{bmatrix}\\right )\\ =\\ \n",
    "\\begin{bmatrix} 2\\cdot 1 + 3\\cdot 0 - 4\\cdot 0 \\end{bmatrix}\\ =\\ \\begin{bmatrix} 2x \\end{bmatrix}$$\n",
    "\n",
    "$$ T\\left ( \\begin{bmatrix} 0 \\\\ 1 \\\\ 0 \\\\ 0 \\end{bmatrix}\\right )\\ =\\ \n",
    "\\begin{bmatrix} 2\\cdot 0 + 3\\cdot 0 - 4\\cdot 0 \\end{bmatrix}\\ =\\ \\begin{bmatrix} 0 \\end{bmatrix}$$\n",
    "\n",
    "$$ T\\left ( \\begin{bmatrix} 0 \\\\ 0 \\\\ 1 \\\\ 0 \\end{bmatrix}\\right )\\ =\\ \n",
    "\\begin{bmatrix} 2\\cdot 0 + 3\\cdot 1 - 4\\cdot 0 \\end{bmatrix}\\ =\\ \\begin{bmatrix} 3 \\end{bmatrix}$$\n",
    "\n",
    "$$ T\\left ( \\begin{bmatrix} 0 \\\\ 0 \\\\ 0 \\\\ 1 \\end{bmatrix}\\right )\\ =\\ \n",
    "\\begin{bmatrix} 2\\cdot 0 + 3\\cdot 0 - 4\\cdot 1\\end{bmatrix}\\ =\\ \\begin{bmatrix} -4 \\end{bmatrix}$$\n",
    "\n",
    "yielding:\n",
    "\n",
    "\n",
    "$$\\begin{bmatrix} 2 & 0 & 3 & -4 \\\\\\end{bmatrix}$$"
   ]
  },
  {
   "attachments": {
    "Screen%20Shot%202021-07-23%20at%203.38.13%20PM.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem 7\n",
    "\n",
    "(A) Find all ${\\bf x}\\in \\mathbb{R}^4$ that are mapped into the zero vector by the transformation ${\\bf x}\\mapsto A{\\bf x}$ for\n",
    "\n",
    "![Screen%20Shot%202021-07-23%20at%203.38.13%20PM.png](attachment:Screen%20Shot%202021-07-23%20at%203.38.13%20PM.png)\n",
    "\n",
    "Show all work, e.g., traces of running the GE algorithm. \n",
    "\n",
    "(B) Let ${\\bf b} = \\begin{bmatrix} -1 \\\\ 3 \\\\ -1 \\\\ 4 \\end{bmatrix}$.  Answer the following question *without* running the GE algorithm on the augmented $A:b$, but by just considering the RREF created in Part A:  **Is ${\\bf b}$ in the span of the columns of $A$?**   Explain carefully why running the GE algorithm again is not necessary to answer the question. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Solution:**\n",
    "\n",
    "(A)  The array reduces to $I_4$, which means that $rank(A)=4$ so $A$ is invertible and $null(A) = {\\bf 0}$,\n",
    "that is only ${\\bf 0}$ is mapped to the zero vector. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.,  0.,  0.,  0.],\n",
       "       [ 0.,  1.,  0.,  0.],\n",
       "       [-0., -0.,  1.,  0.],\n",
       "       [ 0.,  0.,  0.,  1.]])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = np.array(  [[1,3,9,2],[1,0,3,-4],[0,1,2,3],[-1,3,0,5]])\n",
    "GaussianElimination(A)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(B)  $\\bf b$ must be in the span of the columns of A because it is 1-to-1 and onto, so there\n",
    "is a unique vector which is the solution to $A{\\bf x} = {\\bf 0}$. We don't need to run the GE\n",
    "on an augmented matrix to answer the existence question because $A$ is onto, because every row\n",
    "has a pivot, and hence the columns of $A$ span all of $\\mathbb{R}^4$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem 8\n",
    "\n",
    "Transformation $S$ and $T$ *commute* if for every vector $\\bf x$, \n",
    "\n",
    "$$S(T({\\bf x})) \\ = \\ T(S({\\bf x})).$$\n",
    "\n",
    "(A)  Consider the following geometric 2D transformations: \n",
    "\n",
    "- D -- a dilation (in which x-coordinates and y-coordinates are scaled by the same factor $d$); \n",
    "- R -- a rotation (about the origin, for some $\\theta$), \n",
    "- F -- a reflection across the $x$-axis, \n",
    "- S -- a shear (by some factor $f$ in the $x$-direction), \n",
    "\n",
    "Assume each of these transformations is fixed with specific parameters (e.g., a specific line for F, or some $\\theta$ for R).\n",
    "\n",
    "Which pairs of transformations commute? (There are 6 pairs to consider.)  Justify briefly in each case. \n",
    "\n",
    "(B)  Let us define an *x-dilation* as a 2D transformation which multiplies every $x$ value by a scalar $a$,\n",
    "and a *y-dilation* as a 2D transformation which multiplies every $y$ value by a scalar $b$.  Prove/show the\n",
    "following fact:  For any $a$ and $b$, the corresponding x-dilation and y-dilation commute. \n",
    "\n",
    "(C) From your result in Part B, you may conclude *immediately* that a reflection across the x-axis commutes\n",
    "with a reflection across the y-axis.  Why is this the case?\n",
    "\n",
    "Hint: When the professor in your math class asks you to justify/show/explain why, he/she is NOT asking\n",
    "for intuition expressed in English...."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Solution:**\n",
    "\n",
    "Dilation commutes with every other, but no other pairs commute. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "d = 2\n",
    "theta = np.pi/4\n",
    "D = np.array([[2,0],[0,2]])\n",
    "R = np.array([[np.cos(theta),-np.sin(theta)],[np.sin(theta),np.cos(theta)]])\n",
    "F = np.array([[-1,0],[0,1]])\n",
    "S = np.array([[1,1],[0,1]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n",
      "True\n",
      "True\n",
      "False\n",
      "False\n",
      "False\n"
     ]
    }
   ],
   "source": [
    "print( (D @ R == R @ D).all() )\n",
    "print( (D @ F == F @ D).all() )\n",
    "print( (D @ S == S @ D).all() )\n",
    "print( (R @ F == F @ R).all() )\n",
    "print( (R @ S == S @ R).all() )\n",
    "print( (F @ S == S @ F).all() )\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Part B:**\n",
    "\n",
    "If we multiply\n",
    "\n",
    "$$DX = \\begin{bmatrix} a & 0 \\\\ 0 & 1 \\end{bmatrix}$$\n",
    "\n",
    "and\n",
    "\n",
    "$$DY = \\begin{bmatrix} 1 & 0 \\\\ 0 & b \\end{bmatrix}$$\n",
    "\n",
    "in either order, we get the same result:\n",
    "\n",
    "$$\\begin{bmatrix} a & 0 \\\\ 0 & b \\end{bmatrix}.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem 8\n",
    "\n",
    "(A)  Find a  matrix that implements the linear transformation\n",
    "\n",
    "$$T(x,y) = (2y-3x,x-4y,0, y)$$\n",
    "\n",
    "Note that $x$ and $y$ are scalars, and we asking for a matrix $A$ which maps vectors in $\\mathbb{R}^2$ into\n",
    "vectors in $\\mathbb{R}^4$. \n",
    "\n",
    "(B) Find the values for $x$ and $y$ which are mapped to $(-29,-7,0,5)$ by the transformation in (A). \n",
    "\n",
    "\n",
    "(C) Is $T$ *onto*? Explain why or why not.\n",
    "\n",
    "(D) Is $T$ *1-to-1*? Explain why or why not. \n",
    "\n",
    "Hint: For C and D, think about the pivots...."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-3  2]\n",
      " [ 1 -4]\n",
      " [ 0  0]\n",
      " [ 0  1]]\n",
      "[[-29]\n",
      " [ -7]\n",
      " [  0]\n",
      " [  5]]\n"
     ]
    }
   ],
   "source": [
    "# Solution A\n",
    "\n",
    "A = np.array( [[-3,2],[1,-4],[0,0],[0,1]])\n",
    "print(A)\n",
    "\n",
    "# (B) \n",
    "\n",
    "print(A @ np.array( [[13],[5]]))\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Solution (C)\n",
    "\n",
    "No, because the codomain has more dimensions than the domain. There is not a pivot in every row. \n",
    "\n",
    "### Solution (D)\n",
    "\n",
    "Yes, because there is a pivot in every column. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem 9\n",
    "\n",
    "(A) Suppose $(B-C)D = {\\bf 0}$, where $B$ and $C$ are $m\\times n$ matrices and $D$ is invertible. Show that $B =C$.\n",
    "\n",
    "(B)  Suppose $A$ and $B$ are $n\\times n$, $B$ is invertible, and $AB$ is invertible. Show that $A$ is invertible. (Hint: Let\n",
    "$C = AB$, and solve the equation for $A$.)\n",
    "\n",
    "(C) Suppose $P$ is invertible and $A = PBP^{-1}$. Solve for $B$ in terms of $A$.\n",
    "\n",
    "(D) Suppose that $AB = I_n$ and $BC = I_n$. Show that $B=C$. "
   ]
  },
  {
   "attachments": {
    "Screen%20Shot%202021-07-23%20at%204.55.54%20PM.png": {
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Solution:**\n",
    "\n",
    "![Screen%20Shot%202021-07-23%20at%204.55.54%20PM.png](attachment:Screen%20Shot%202021-07-23%20at%204.55.54%20PM.png)\n",
    "\n",
    "(D)  A = AI = ABC = IC = C"
   ]
  }
 ],
 "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": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}