diff --git a/Copy_of_LS_DS_131_Vectors_and_Matrices_Assignment.ipynb b/Copy_of_LS_DS_131_Vectors_and_Matrices_Assignment.ipynb
new file mode 100644
index 00000000..b1499f49
--- /dev/null
+++ b/Copy_of_LS_DS_131_Vectors_and_Matrices_Assignment.ipynb
@@ -0,0 +1,1349 @@
+{
+  "nbformat": 4,
+  "nbformat_minor": 0,
+  "metadata": {
+    "colab": {
+      "name": "Copy of LS_DS_131_Vectors_and_Matrices_Assignment.ipynb",
+      "provenance": [],
+      "collapsed_sections": [],
+      "include_colab_link": true
+    },
+    "kernelspec": {
+      "name": "python3",
+      "display_name": "Python 3"
+    }
+  },
+  "cells": [
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "view-in-github",
+        "colab_type": "text"
+      },
+      "source": [
+        "<a href=\"https://colab.research.google.com/github/Vgrams05/DS-Unit-1-Sprint-3-Linear-Algebra/blob/master/Copy_of_LS_DS_131_Vectors_and_Matrices_Assignment.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "yXA3GwWhY9KL",
+        "colab_type": "text"
+      },
+      "source": [
+        "# Part 1 - Scalars and Vectors\n",
+        "\n",
+        "For the questions below it is not sufficient to simply provide answer to the questions, but you must solve the problems and show your work using python (the NumPy library will help a lot!) Translate the vectors and matrices into their appropriate python  representations and use numpy or functions that you write yourself to demonstrate the result or property. "
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "oNOTv43_Zi9L",
+        "colab_type": "text"
+      },
+      "source": [
+        "## 1.1 Create a two-dimensional vector and plot it on a graph"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "metadata": {
+        "id": "XNqjzQzrkVG7",
+        "colab_type": "code",
+        "colab": {}
+      },
+      "source": [
+        "import matplotlib.pyplot as plt\n",
+        "import numpy as np\n",
+        "import pandas as pd\n",
+        "import math"
+      ],
+      "execution_count": 2,
+      "outputs": []
+    },
+    {
+      "cell_type": "code",
+      "metadata": {
+        "id": "SyObrCGKU0O0",
+        "colab_type": "code",
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 51
+        },
+        "outputId": "c87abfe6-701e-411f-bea4-43bbd90fceda"
+      },
+      "source": [
+        "array_input = [ [.1, .12, .14] ,[0, .1, .2]]\n",
+        "print (array_input[0])\n",
+        "print (array_input[1])"
+      ],
+      "execution_count": 25,
+      "outputs": [
+        {
+          "output_type": "stream",
+          "text": [
+            "[0.1, 0.12, 0.14]\n",
+            "[0, 0.1, 0.2]\n"
+          ],
+          "name": "stdout"
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "metadata": {
+        "id": "qk7ury_VXEc2",
+        "colab_type": "code",
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 269
+        },
+        "outputId": "720fe6c0-19fd-44f0-fe4d-e0bab0b7a476"
+      },
+      "source": [
+        "plt.imshow(array_input)\n",
+        "plt.show()"
+      ],
+      "execution_count": 26,
+      "outputs": [
+        {
+          "output_type": "display_data",
+          "data": {
+            "image/png": "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\n",
+            "text/plain": [
+              "<Figure size 432x288 with 1 Axes>"
+            ]
+          },
+          "metadata": {
+            "tags": [],
+            "needs_background": "light"
+          }
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "metadata": {
+        "id": "EFIeitHrYFoV",
+        "colab_type": "code",
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 34
+        },
+        "outputId": "93ea5499-ae60-406b-a01d-913baf3e91ae"
+      },
+      "source": [
+        "array_input1 = [ [20,22,24] ,[5,6,7], [8,9,10]]\n",
+        "print (array_input1)"
+      ],
+      "execution_count": 14,
+      "outputs": [
+        {
+          "output_type": "stream",
+          "text": [
+            "[[20, 22, 24], [5, 6, 7], [8, 9, 10]]\n"
+          ],
+          "name": "stdout"
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "metadata": {
+        "id": "EXUwP9lYYPPE",
+        "colab_type": "code",
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 269
+        },
+        "outputId": "64028975-c609-409e-b4f8-81120fd171d9"
+      },
+      "source": [
+        "plt.imshow(array_input1)\n",
+        "plt.show()"
+      ],
+      "execution_count": 15,
+      "outputs": [
+        {
+          "output_type": "display_data",
+          "data": {
+            "image/png": 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JRU5ErkJggg==\n",
+            "text/plain": [
+              "<Figure size 432x288 with 1 Axes>"
+            ]
+          },
+          "metadata": {
+            "tags": [],
+            "needs_background": "light"
+          }
+        }
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "unKFT619lk3e",
+        "colab_type": "text"
+      },
+      "source": [
+        "## 1.2 Create a three-dimensional vecor and plot it on a graph"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "metadata": {
+        "id": "atUEd3T6llKm",
+        "colab_type": "code",
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 248
+        },
+        "outputId": "5f4542ce-675a-46a6-b666-43915441cb7e"
+      },
+      "source": [
+        "pink = [.6, .6, .6]\n",
+        "blue = [.3, .2, .1]\n",
+        "white = [.2, .4, .4]\n",
+        "\n",
+        "vectors =np.array([[0, 0, 0, .6, .6, .6],\n",
+        "                  [0, 0, 0, .3, .2, .1],\n",
+        "                  [0, 0, 0, .2, .4, .4]])\n",
+        "\n",
+        "X, Y, Z, U, V, W = zip(*vectors)\n",
+        "fig = plt.figure()\n",
+        "ax = fig.add_subplot(111, projection='3d')\n",
+        "ax.quiver(X, Y, Z, U, V, W, length=1)\n",
+        "ax.set_xlim([0, 1])\n",
+        "ax.set_ylim([0, 1])\n",
+        "ax.set_zlim([0, 1])\n",
+        "ax.set_xlabel('X')\n",
+        "ax.set_ylabel('Y')\n",
+        "ax.set_zlabel('Z')\n",
+        "plt.show()"
+      ],
+      "execution_count": 17,
+      "outputs": [
+        {
+          "output_type": "display_data",
+          "data": {
+            "image/png": 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\n",
+            "text/plain": [
+              "<Figure size 432x288 with 1 Axes>"
+            ]
+          },
+          "metadata": {
+            "tags": [],
+            "needs_background": "light"
+          }
+        }
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "b7qFxbKxZmI2",
+        "colab_type": "text"
+      },
+      "source": [
+        "## 1.3 Scale the vectors you created in 1.1 by $5$, $\\pi$, and $-e$ and plot all four vectors (original + 3 scaled vectors) on a graph. What do you notice about these vectors? "
+      ]
+    },
+    {
+      "cell_type": "code",
+      "metadata": {
+        "id": "ah6zMSLJdJwL",
+        "colab_type": "code",
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 51
+        },
+        "outputId": "1c9b6769-60ef-4687-aa3a-35e02fd58980"
+      },
+      "source": [
+        "from math import e, pi\n",
+        "print(e)\n",
+        "print(pi)"
+      ],
+      "execution_count": 18,
+      "outputs": [
+        {
+          "output_type": "stream",
+          "text": [
+            "2.718281828459045\n",
+            "3.141592653589793\n"
+          ],
+          "name": "stdout"
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "metadata": {
+        "id": "3qpwDlzXkVf5",
+        "colab_type": "code",
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 643
+        },
+        "outputId": "886d6615-0265-4eb3-d632-87e85b214afe"
+      },
+      "source": [
+        "g = np.multiply(5, array_input)\n",
+        "\n",
+        "r = np.multiply(math.pi, array_input)\n",
+        "\n",
+        "o = np.multiply(math.e, array_input)\n",
+        "\n",
+        "plt.arrow (0,0, r[0], r[1],head_width=.05,head_length=0.05, color='red')\n",
+        "plt.arrow (0,0, g[0], g[1],head_width=.05, head_length=0.05, color='green')\n",
+        "plt.arrow(0,0, array_input[0], array_input[1],head_width=.05, head_length=0.05, color ='blue')\n",
+        "plt.arrow (0,0, o[0], o[1],head_width=.05, head_length=0.05, color='orange')\n",
+        "plt.xlim(1,2)\n",
+        "plt.ylim(1,2)\n",
+        "plt.show()"
+      ],
+      "execution_count": 29,
+      "outputs": [
+        {
+          "output_type": "error",
+          "ename": "ValueError",
+          "evalue": "ignored",
+          "traceback": [
+            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+            "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
+            "\u001b[0;32m<ipython-input-29-47bff104a9ea>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0mo\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmultiply\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmath\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0me\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0marray_input\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      6\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 7\u001b[0;31m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marrow\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mr\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mr\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mhead_width\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m.05\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mhead_length\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0.05\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcolor\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'red'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      8\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marrow\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mg\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mg\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mhead_width\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m.05\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mhead_length\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0.05\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcolor\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'green'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      9\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marrow\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0marray_input\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0marray_input\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mhead_width\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m.05\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mhead_length\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0.05\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcolor\u001b[0m \u001b[0;34m=\u001b[0m\u001b[0;34m'blue'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+            "\u001b[0;32m/usr/local/lib/python3.6/dist-packages/matplotlib/pyplot.py\u001b[0m in \u001b[0;36marrow\u001b[0;34m(x, y, dx, dy, **kwargs)\u001b[0m\n\u001b[1;32m   2361\u001b[0m \u001b[0;34m@\u001b[0m\u001b[0mdocstring\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcopy\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mAxes\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marrow\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2362\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0marrow\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdy\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 2363\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0mgca\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marrow\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdy\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   2364\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2365\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
+            "\u001b[0;32m/usr/local/lib/python3.6/dist-packages/matplotlib/axes/_axes.py\u001b[0m in \u001b[0;36marrow\u001b[0;34m(self, x, y, dx, dy, **kwargs)\u001b[0m\n\u001b[1;32m   4950\u001b[0m         \u001b[0mdy\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mconvert_yunits\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdy\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   4951\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 4952\u001b[0;31m         \u001b[0ma\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmpatches\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mFancyArrow\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdy\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   4953\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0madd_artist\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   4954\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+            "\u001b[0;32m/usr/local/lib/python3.6/dist-packages/matplotlib/patches.py\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, x, y, dx, dy, width, length_includes_head, head_width, head_length, shape, overhang, head_starts_at_zero, **kwargs)\u001b[0m\n\u001b[1;32m   1285\u001b[0m         \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1286\u001b[0m             \u001b[0mlength\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdistance\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mhead_length\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1287\u001b[0;31m         \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mlength\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1288\u001b[0m             \u001b[0mverts\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mempty\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m  \u001b[0;31m# display nothing if empty\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1289\u001b[0m         \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+            "\u001b[0;31mValueError\u001b[0m: The truth value of an array with more than one element is ambiguous. Use a.any() or a.all()"
+          ]
+        },
+        {
+          "output_type": "display_data",
+          "data": {
+            "image/png": "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\n",
+            "text/plain": [
+              "<Figure size 432x288 with 1 Axes>"
+            ]
+          },
+          "metadata": {
+            "tags": [],
+            "needs_background": "light"
+          }
+        }
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "wrgqa6sWimbH",
+        "colab_type": "text"
+      },
+      "source": [
+        "## 1.4 Graph vectors $\\vec{a}$ and $\\vec{b}$ and plot them on a graph\n",
+        "\n",
+        "\\begin{align}\n",
+        "\\vec{a} = \\begin{bmatrix} 5 \\\\ 7 \\end{bmatrix}\n",
+        "\\qquad\n",
+        "\\vec{b} = \\begin{bmatrix} 3 \\\\4 \\end{bmatrix}\n",
+        "\\end{align}"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "metadata": {
+        "id": "I1BGXA_skV-b",
+        "colab_type": "code",
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 269
+        },
+        "outputId": "23d475ce-6c71-4422-a814-53ba69c5e4f1"
+      },
+      "source": [
+        "v = ([[5, 7],\n",
+        "      [3, 4]])\n",
+        "\n",
+        "plt.arrow(0, 0, 5, 7, head_width=.02, head_length=0.01, color = \"r\")\n",
+        "plt.arrow(0, 0, 3, 4, head_width=.02, head_length=0.01, color = \"b\")\n",
+        "plt.show()"
+      ],
+      "execution_count": 34,
+      "outputs": [
+        {
+          "output_type": "display_data",
+          "data": {
+            "image/png": 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\n",
+            "text/plain": [
+              "<Figure size 432x288 with 1 Axes>"
+            ]
+          },
+          "metadata": {
+            "tags": [],
+            "needs_background": "light"
+          }
+        }
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "QN6RU_3gizpw",
+        "colab_type": "text"
+      },
+      "source": [
+        "## 1.5 find $\\vec{a} - \\vec{b}$ and plot the result on the same graph as $\\vec{a}$ and $\\vec{b}$. Is there a relationship between vectors $\\vec{a} \\thinspace, \\vec{b} \\thinspace \\text{and} \\thinspace \\vec{a-b}$"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "metadata": {
+        "id": "68sWHIOPkXp5",
+        "colab_type": "code",
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 34
+        },
+        "outputId": "477d507d-8f96-4dfc-8388-9a350bbb8db8"
+      },
+      "source": [
+        "a = ([5,7])\n",
+        "b = ([3,4])\n",
+        "\n",
+        "np.subtract(a, b)"
+      ],
+      "execution_count": 37,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "array([2, 3])"
+            ]
+          },
+          "metadata": {
+            "tags": []
+          },
+          "execution_count": 37
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "metadata": {
+        "id": "3Eg2rDz2hro6",
+        "colab_type": "code",
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 269
+        },
+        "outputId": "23862437-437a-4c84-aff7-37f3bbb3aaa0"
+      },
+      "source": [
+        "plt.arrow(0, 0, 5, 7, head_width=.02, head_length=0.01, color = \"r\")\n",
+        "plt.arrow(0, 0, 3, 4, head_width=.02, head_length=0.01, color = \"b\")\n",
+        "plt.arrow(0, 0, 2, 3, head_width=.02, head_length=0.01, color = \"g\")\n",
+        "\n",
+        "plt.show()"
+      ],
+      "execution_count": 38,
+      "outputs": [
+        {
+          "output_type": "display_data",
+          "data": {
+            "image/png": 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\n",
+            "text/plain": [
+              "<Figure size 432x288 with 1 Axes>"
+            ]
+          },
+          "metadata": {
+            "tags": [],
+            "needs_background": "light"
+          }
+        }
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "1ZPVuJAlehu_",
+        "colab_type": "text"
+      },
+      "source": [
+        "## 1.6 Find $c \\cdot d$\n",
+        "\n",
+        "\\begin{align}\n",
+        "\\vec{c} = \\begin{bmatrix}7 & 22 & 4 & 16\\end{bmatrix}\n",
+        "\\qquad\n",
+        "\\vec{d} = \\begin{bmatrix}12 & 6 & 2 & 9\\end{bmatrix}\n",
+        "\\end{align}\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "metadata": {
+        "id": "2_cZQFCskYNr",
+        "colab_type": "code",
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 34
+        },
+        "outputId": "398c165d-aa99-4bd7-a52f-a14209f4d4ed"
+      },
+      "source": [
+        "c = ([7, 22, 4, 16])\n",
+        "d = ([12, 6, 2, 9])\n",
+        "\n",
+        "np.multiply(c, d)"
+      ],
+      "execution_count": 39,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "array([ 84, 132,   8, 144])"
+            ]
+          },
+          "metadata": {
+            "tags": []
+          },
+          "execution_count": 39
+        }
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "cLm8yokpfg9B",
+        "colab_type": "text"
+      },
+      "source": [
+        "##  1.7 Find $e \\times f$\n",
+        "\n",
+        "\\begin{align}\n",
+        "\\vec{e} = \\begin{bmatrix} 5 \\\\ 7 \\\\ 2 \\end{bmatrix}\n",
+        "\\qquad\n",
+        "\\vec{f} = \\begin{bmatrix} 3 \\\\4 \\\\ 6 \\end{bmatrix}\n",
+        "\\end{align}"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "metadata": {
+        "id": "ku-TdCKAkYs8",
+        "colab_type": "code",
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 34
+        },
+        "outputId": "149b7bc8-d81a-4564-9774-ad30bbd75c46"
+      },
+      "source": [
+        "e = ([5,\n",
+        "      7,\n",
+        "      2])\n",
+        "f = ([3,\n",
+        "      4,\n",
+        "      6])\n",
+        "\n",
+        "np.multiply(e, f)"
+      ],
+      "execution_count": 40,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "array([15, 28, 12])"
+            ]
+          },
+          "metadata": {
+            "tags": []
+          },
+          "execution_count": 40
+        }
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "-TN8wO2-h53s",
+        "colab_type": "text"
+      },
+      "source": [
+        "## 1.8 Find $||g||$ and then find $||h||$. Which is longer?\n",
+        "\n",
+        "\\begin{align}\n",
+        "\\vec{g} = \\begin{bmatrix} 1 \\\\ 1 \\\\ 1 \\\\ 8 \\end{bmatrix}\n",
+        "\\qquad\n",
+        "\\vec{h} = \\begin{bmatrix} 3 \\\\3 \\\\ 3 \\\\ 3 \\end{bmatrix}\n",
+        "\\end{align}"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "metadata": {
+        "id": "-5VKOMKBlgaA",
+        "colab_type": "code",
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 269
+        },
+        "outputId": "2460e39e-4157-48b8-96ba-13bf966e9b4b"
+      },
+      "source": [
+        "g = ([1, 1, 1, 8])\n",
+        "h = ([3, 3, 3, 3])\n",
+        "\n",
+        "plt.arrow(0, 0, 2, 7, head_width=.02, head_length=0.01, color = \"r\")\n",
+        "plt.arrow(0, 0, 6, 6, head_width=.02, head_length=0.01, color = \"b\")\n",
+        "\n",
+        "plt.show()"
+      ],
+      "execution_count": 43,
+      "outputs": [
+        {
+          "output_type": "display_data",
+          "data": {
+            "image/png": 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\n",
+            "text/plain": [
+              "<Figure size 432x288 with 1 Axes>"
+            ]
+          },
+          "metadata": {
+            "tags": [],
+            "needs_background": "light"
+          }
+        }
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "yw5BnK4rmBDc",
+        "colab_type": "text"
+      },
+      "source": [
+        "**H vector is long than G vector**"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "njrWIMS-ZAoH",
+        "colab_type": "text"
+      },
+      "source": [
+        "# Part 2 - Matrices"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "GjkcAVIOmOnn",
+        "colab_type": "text"
+      },
+      "source": [
+        "## 2.1 What are the dimensions of the following matrices? Which of the following can be multiplied together? See if you can find all of the different legal combinations.\n",
+        "\\begin{align}\n",
+        "A = \\begin{bmatrix}\n",
+        "1 & 2 \\\\\n",
+        "3 & 4 \\\\\n",
+        "5 & 6\n",
+        "\\end{bmatrix}\n",
+        "\\qquad\n",
+        "B = \\begin{bmatrix}\n",
+        "2 & 4 & 6 \\\\\n",
+        "\\end{bmatrix}\n",
+        "\\qquad\n",
+        "C = \\begin{bmatrix}\n",
+        "9 & 6 & 3 \\\\\n",
+        "4 & 7 & 11\n",
+        "\\end{bmatrix}\n",
+        "\\qquad\n",
+        "D = \\begin{bmatrix}\n",
+        "1 & 0 & 0 \\\\\n",
+        "0 & 1 & 0 \\\\\n",
+        "0 & 0 & 1\n",
+        "\\end{bmatrix}\n",
+        "\\qquad\n",
+        "E = \\begin{bmatrix}\n",
+        "1 & 3 \\\\\n",
+        "5 & 7\n",
+        "\\end{bmatrix}\n",
+        "\\end{align}"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "metadata": {
+        "id": "g2H8ZmBtoYL6",
+        "colab_type": "code",
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 34
+        },
+        "outputId": "1be72357-4cc5-41d7-f11e-91b283261642"
+      },
+      "source": [
+        "a = ([[1, 2],\n",
+        "     [3, 4],\n",
+        "      [5, 6]])\n",
+        "\n",
+        "rows = len(a)\n",
+        "columns = len(a[0])\n",
+        "\n",
+        "print (\"A's dimension is: \", rows, columns)"
+      ],
+      "execution_count": 52,
+      "outputs": [
+        {
+          "output_type": "stream",
+          "text": [
+            "A's dimension is:  3 2\n"
+          ],
+          "name": "stdout"
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "metadata": {
+        "id": "AUt5ZmrtpCd2",
+        "colab_type": "code",
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 34
+        },
+        "outputId": "c9125ee8-dc27-41d4-c928-01e01c5250f0"
+      },
+      "source": [
+        "b = ([2, 4, 6])\n",
+        "\n",
+        "rows = len(b)\n",
+        "\n",
+        "\n",
+        "print (\"B's dimension is: \", rows)"
+      ],
+      "execution_count": 55,
+      "outputs": [
+        {
+          "output_type": "stream",
+          "text": [
+            "B's dimension is:  3\n"
+          ],
+          "name": "stdout"
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "metadata": {
+        "id": "OX7hybnapTVz",
+        "colab_type": "code",
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 34
+        },
+        "outputId": "1ddd793b-bb0e-497e-a260-591cae07fb3d"
+      },
+      "source": [
+        "c = ([[9, 4, 3],\n",
+        "      [4, 7, 11]])\n",
+        "\n",
+        "rows = len(c)\n",
+        "columns = len(c[0])\n",
+        "\n",
+        "print (\"C's dimension is: \", rows, columns)"
+      ],
+      "execution_count": 56,
+      "outputs": [
+        {
+          "output_type": "stream",
+          "text": [
+            "C's dimension is:  2 3\n"
+          ],
+          "name": "stdout"
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "metadata": {
+        "id": "ZEbnmbI9plHG",
+        "colab_type": "code",
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 34
+        },
+        "outputId": "260026e8-3a7e-4d77-f27a-e1bbea4ececd"
+      },
+      "source": [
+        "d = ([[1, 0, 0],\n",
+        "      [0, 1, 0],\n",
+        "      [0, 0, 1]])\n",
+        "\n",
+        "rows = len(d)\n",
+        "columns = len(d[0])\n",
+        "\n",
+        "print (\"D's dimension is: \", rows, columns)"
+      ],
+      "execution_count": 57,
+      "outputs": [
+        {
+          "output_type": "stream",
+          "text": [
+            "D's dimension is:  3 3\n"
+          ],
+          "name": "stdout"
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "metadata": {
+        "id": "UVEALkXVp1X4",
+        "colab_type": "code",
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 34
+        },
+        "outputId": "da713228-5f8e-4ce9-a3bb-b9b99a190820"
+      },
+      "source": [
+        "e = ([[1, 3],\n",
+        "      [5, 7]])\n",
+        "\n",
+        "rows = len(e)\n",
+        "columns = len(e[0])\n",
+        "\n",
+        "print (\"E's dimension is: \", rows, columns)"
+      ],
+      "execution_count": 58,
+      "outputs": [
+        {
+          "output_type": "stream",
+          "text": [
+            "E's dimension is:  2 2\n"
+          ],
+          "name": "stdout"
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "metadata": {
+        "id": "Z69c-uPtnbIx",
+        "colab_type": "code",
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 68
+        },
+        "outputId": "8b07cf3b-92d9-453f-a973-eacd1ffd3e23"
+      },
+      "source": [
+        "import numpy as np\n",
+        "a = np.array([[1, 2],\n",
+        "     [3, 4],\n",
+        "      [5, 6]])\n",
+        "c = np.array([[9, 4, 3],\n",
+        "              [4, 7, 11]])\n",
+        "\n",
+        "np.matmul(a, c)"
+      ],
+      "execution_count": 50,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "array([[17, 18, 25],\n",
+              "       [43, 40, 53],\n",
+              "       [69, 62, 81]])"
+            ]
+          },
+          "metadata": {
+            "tags": []
+          },
+          "execution_count": 50
+        }
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "lMOlCoM3ncGa",
+        "colab_type": "text"
+      },
+      "source": [
+        "## 2.2 Find the following products: CD, AE, and BA. What are the dimensions of the resulting matrices? How does that relate to the dimensions of their factor matrices?"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "metadata": {
+        "id": "zhKwiSItoE2F",
+        "colab_type": "code",
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 51
+        },
+        "outputId": "a2f79d0d-bf12-4c79-9e8b-ade736b6ffc5"
+      },
+      "source": [
+        "cd= np.matmul(c, d)\n",
+        "\n",
+        "cd"
+      ],
+      "execution_count": 64,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "array([[ 9,  4,  3],\n",
+              "       [ 4,  7, 11]])"
+            ]
+          },
+          "metadata": {
+            "tags": []
+          },
+          "execution_count": 64
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "metadata": {
+        "id": "r38kld5arU6J",
+        "colab_type": "code",
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 34
+        },
+        "outputId": "b3f3a26e-6c0f-4647-941b-aca8c3652862"
+      },
+      "source": [
+        "rows = len(cd)\n",
+        "columns = len(cd[0])\n",
+        "\n",
+        "print (\"CD's dimension is: \", rows, columns )"
+      ],
+      "execution_count": 65,
+      "outputs": [
+        {
+          "output_type": "stream",
+          "text": [
+            "CD's dimension is:  2 3\n"
+          ],
+          "name": "stdout"
+        }
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "Tj9ClVcvrAyG",
+        "colab_type": "text"
+      },
+      "source": [
+        "**The new matrices does not relate to D in dimension but it does relate to C in dimension**"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "metadata": {
+        "id": "07g-CdJVqzrD",
+        "colab_type": "code",
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 68
+        },
+        "outputId": "ca099ec0-5779-44c6-b43c-1636dbb1987a"
+      },
+      "source": [
+        "AE = np.matmul(a, e)\n",
+        "\n",
+        "AE"
+      ],
+      "execution_count": 66,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "array([[11, 17],\n",
+              "       [23, 37],\n",
+              "       [35, 57]])"
+            ]
+          },
+          "metadata": {
+            "tags": []
+          },
+          "execution_count": 66
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "metadata": {
+        "id": "tVhjbQjrsMr6",
+        "colab_type": "code",
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 34
+        },
+        "outputId": "a479a25e-079d-4d82-dee0-ae7b0838e6a7"
+      },
+      "source": [
+        "rows = len(AE)\n",
+        "columns = len(AE[0])\n",
+        "\n",
+        "print (\"AE's dimension is: \", rows, columns)"
+      ],
+      "execution_count": 67,
+      "outputs": [
+        {
+          "output_type": "stream",
+          "text": [
+            "AE's dimension is:  3 2\n"
+          ],
+          "name": "stdout"
+        }
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "XAmw1P6JshJn",
+        "colab_type": "text"
+      },
+      "source": [
+        "**The new matrices (AE) does not relate to E dimension but does relate to A dimension**"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "metadata": {
+        "id": "7M4gPzH8q4HO",
+        "colab_type": "code",
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 34
+        },
+        "outputId": "8d4ddc58-1fc8-4737-b800-672183a6594e"
+      },
+      "source": [
+        "BA = np.matmul(b, a)\n",
+        "\n",
+        "BA"
+      ],
+      "execution_count": 68,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "array([44, 56])"
+            ]
+          },
+          "metadata": {
+            "tags": []
+          },
+          "execution_count": 68
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "metadata": {
+        "id": "caqVPdBfs3iA",
+        "colab_type": "code",
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 34
+        },
+        "outputId": "94d9defb-c91c-492f-f5c6-e70476d9cc17"
+      },
+      "source": [
+        "columns = len(BA)\n",
+        "\n",
+        "print (\"BA's dimension is: \", columns)"
+      ],
+      "execution_count": 72,
+      "outputs": [
+        {
+          "output_type": "stream",
+          "text": [
+            "BA's dimension is:  2\n"
+          ],
+          "name": "stdout"
+        }
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "QyWakU60tk0b",
+        "colab_type": "text"
+      },
+      "source": [
+        "**The new matrices (BA) does relate to B dimension by by being one row, and relates to A dimension by having two columns**"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "p2jmaGLgoFPN",
+        "colab_type": "text"
+      },
+      "source": [
+        "## 2.3  Find $F^{T}$. How are the numbers along the main diagonal (top left to bottom right) of the original matrix and its transpose related? What are the dimensions of $F$? What are the dimensions of $F^{T}$?\n",
+        "\n",
+        "\\begin{align}\n",
+        "F = \n",
+        "\\begin{bmatrix}\n",
+        "20 & 19 & 18 & 17 \\\\\n",
+        "16 & 15 & 14 & 13 \\\\\n",
+        "12 & 11 & 10 & 9 \\\\\n",
+        "8 & 7 & 6 & 5 \\\\\n",
+        "4 & 3 & 2 & 1\n",
+        "\\end{bmatrix}\n",
+        "\\end{align}"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "metadata": {
+        "id": "BTRHnRuxwIoT",
+        "colab_type": "code",
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 34
+        },
+        "outputId": "17346bff-9db3-4add-d21c-eebcd73b6371"
+      },
+      "source": [
+        "len(F)"
+      ],
+      "execution_count": 77,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "5"
+            ]
+          },
+          "metadata": {
+            "tags": []
+          },
+          "execution_count": 77
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "metadata": {
+        "id": "Wl3ElwgLqaAn",
+        "colab_type": "code",
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 85
+        },
+        "outputId": "a43bfe5b-1d04-4df8-dd8c-406cb56438ba"
+      },
+      "source": [
+        "F = ([[20, 19, 18, 17],\n",
+        "      [16, 15, 14, 13],\n",
+        "      [12, 11, 10, 9],\n",
+        "      [8, 7, 6, 5],\n",
+        "      [4, 3, 2, 1]])\n",
+        "\n",
+        "FT = np.transpose(F)\n",
+        "\n",
+        "FT"
+      ],
+      "execution_count": 76,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "array([[20, 16, 12,  8,  4],\n",
+              "       [19, 15, 11,  7,  3],\n",
+              "       [18, 14, 10,  6,  2],\n",
+              "       [17, 13,  9,  5,  1]])"
+            ]
+          },
+          "metadata": {
+            "tags": []
+          },
+          "execution_count": 76
+        }
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "13ik2LEEZLHn",
+        "colab_type": "text"
+      },
+      "source": [
+        "# Part 3 - Square Matrices"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "sDBAPUwfp7f7",
+        "colab_type": "text"
+      },
+      "source": [
+        "## 3.1 Find $IG$ (be sure to show your work) 😃\n",
+        "\n",
+        "You don't have to do anything crazy complicated here to show your work, just create the G matrix as specified below, and a corresponding 2x2 Identity matrix and then multiply them together to show the result. You don't need to write LaTeX or anything like that (unless you want to).\n",
+        "\n",
+        "\\begin{align}\n",
+        "G= \n",
+        "\\begin{bmatrix}\n",
+        "13 & 14 \\\\\n",
+        "21 & 12 \n",
+        "\\end{bmatrix}\n",
+        "\\end{align}"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "metadata": {
+        "id": "ZnqvZBOYqar3",
+        "colab_type": "code",
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 51
+        },
+        "outputId": "a835103f-14c2-4cc2-f7f2-5c9200c98ecd"
+      },
+      "source": [
+        "G = np.array([[13, 14],\n",
+        "              [21, 12]])\n",
+        "I =  np.array([[11, 12],\n",
+        "              [23, 13]])\n",
+        "\n",
+        "np.matmul(G, I)"
+      ],
+      "execution_count": 73,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "array([[465, 338],\n",
+              "       [507, 408]])"
+            ]
+          },
+          "metadata": {
+            "tags": []
+          },
+          "execution_count": 73
+        }
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "DZ_0XTDQqpMT",
+        "colab_type": "text"
+      },
+      "source": [
+        "## 3.2 Find $|H|$ and then find $|J|$.\n",
+        "\n",
+        "\\begin{align}\n",
+        "H= \n",
+        "\\begin{bmatrix}\n",
+        "12 & 11 \\\\\n",
+        "7 & 10 \n",
+        "\\end{bmatrix}\n",
+        "\\qquad\n",
+        "J= \n",
+        "\\begin{bmatrix}\n",
+        "0 & 1 & 2 \\\\\n",
+        "7 & 10 & 4 \\\\\n",
+        "3 & 2 & 0\n",
+        "\\end{bmatrix}\n",
+        "\\end{align}\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "metadata": {
+        "id": "5QShhoXyrjDS",
+        "colab_type": "code",
+        "colab": {}
+      },
+      "source": [
+        ""
+      ],
+      "execution_count": null,
+      "outputs": []
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "2gZl1CFwrXSH",
+        "colab_type": "text"
+      },
+      "source": [
+        "## 3.3 Find $H^{-1}$ and then find $J^{-1}$"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "metadata": {
+        "id": "nyX6De2-rio1",
+        "colab_type": "code",
+        "colab": {}
+      },
+      "source": [
+        ""
+      ],
+      "execution_count": null,
+      "outputs": []
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "Vvd4Pe86rjhW",
+        "colab_type": "text"
+      },
+      "source": [
+        "## 3.4 Find $HH^{-1}$ and then find $J^{-1}J$. Is $HH^{-1} == J^{-1}J$? Why or Why not? \n",
+        "\n",
+        "Please ignore Python rounding errors. If necessary, format your output so that it rounds to 5 significant digits (the fifth decimal place)."
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "V0iTO4McYjtk",
+        "colab_type": "text"
+      },
+      "source": [
+        "# Stretch Goals: \n",
+        "\n",
+        "A reminder that these challenges are optional. If you finish your work quickly we welcome you to work on them. If there are other activities that you feel like will help your understanding of the above topics more, feel free to work on that. Topics from the Stretch Goals sections will never end up on Sprint Challenges. You don't have to do these in order, you don't have to do all of them. \n",
+        "\n",
+        "- Write a function that can calculate the dot product of any two vectors of equal length that are passed to it.\n",
+        "- Write a function that can calculate the norm of any vector\n",
+        "- Prove to yourself again that the vectors in 1.9 are orthogonal by graphing them. \n",
+        "- Research how to plot a 3d graph with animations so that you can make the graph rotate (this will be easier in a local notebook than in google colab)\n",
+        "- Create and plot a matrix on a 2d graph.\n",
+        "- Create and plot a matrix on a 3d graph.\n",
+        "- Plot two vectors that are not collinear on a 2d graph. Calculate the determinant of the 2x2 matrix that these vectors form. How does this determinant relate to the graphical interpretation of the vectors?\n",
+        "\n"
+      ]
+    }
+  ]
+}
\ No newline at end of file
diff --git a/module1-vectors-and-matrices/LS_DS_131_Vectors_and_Matrices_Assignment.ipynb b/module1-vectors-and-matrices/LS_DS_131_Vectors_and_Matrices_Assignment.ipynb
index 87fc432d..2a08bf5f 100644
--- a/module1-vectors-and-matrices/LS_DS_131_Vectors_and_Matrices_Assignment.ipynb
+++ b/module1-vectors-and-matrices/LS_DS_131_Vectors_and_Matrices_Assignment.ipynb
@@ -5,7 +5,11 @@
     "colab": {
       "name": "LS_DS_131_Vectors_and_Matrices_Assignment.ipynb",
       "provenance": [],
-      "collapsed_sections": []
+      "collapsed_sections": [
+        "Vvd4Pe86rjhW",
+        "V0iTO4McYjtk"
+      ],
+      "include_colab_link": true
     },
     "kernelspec": {
       "name": "python3",
@@ -13,6 +17,16 @@
     }
   },
   "cells": [
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "view-in-github",
+        "colab_type": "text"
+      },
+      "source": [
+        "<a href=\"https://colab.research.google.com/github/Vgrams05/DS-Unit-1-Sprint-3-Linear-Algebra/blob/master/module1-vectors-and-matrices/LS_DS_131_Vectors_and_Matrices_Assignment.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
+      ]
+    },
     {
       "cell_type": "markdown",
       "metadata": {
@@ -43,11 +57,51 @@
         "colab": {}
       },
       "source": [
-        ""
+        "import matplotlib.pyplot as plt\n",
+        "import numpy as np\n",
+        "import pandas as pd\n",
+        "import math"
       ],
-      "execution_count": 0,
+      "execution_count": 2,
       "outputs": []
     },
+    {
+      "cell_type": "code",
+      "metadata": {
+        "id": "SyObrCGKU0O0",
+        "colab_type": "code",
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 269
+        },
+        "outputId": "c628de17-9a6b-46c3-e191-0bd698aed6eb"
+      },
+      "source": [
+        "p = ([.5, .6])\n",
+        "\n",
+        "\n",
+        "plt.arrow(0, 0, .5, .6, head_width=.02, head_length=0.01, color = 'y')\n",
+        "\n",
+        "\n",
+        "plt.show()"
+      ],
+      "execution_count": 96,
+      "outputs": [
+        {
+          "output_type": "display_data",
+          "data": {
+            "image/png": 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\n",
+            "text/plain": [
+              "<Figure size 432x288 with 1 Axes>"
+            ]
+          },
+          "metadata": {
+            "tags": [],
+            "needs_background": "light"
+          }
+        }
+      ]
+    },
     {
       "cell_type": "markdown",
       "metadata": {
@@ -63,13 +117,49 @@
       "metadata": {
         "id": "atUEd3T6llKm",
         "colab_type": "code",
-        "colab": {}
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 248
+        },
+        "outputId": "5f4542ce-675a-46a6-b666-43915441cb7e"
       },
       "source": [
-        ""
+        "pink = [.6, .6, .6]\n",
+        "blue = [.3, .2, .1]\n",
+        "white = [.2, .4, .4]\n",
+        "\n",
+        "vectors =np.array([[0, 0, 0, .6, .6, .6],\n",
+        "                  [0, 0, 0, .3, .2, .1],\n",
+        "                  [0, 0, 0, .2, .4, .4]])\n",
+        "\n",
+        "X, Y, Z, U, V, W = zip(*vectors)\n",
+        "fig = plt.figure()\n",
+        "ax = fig.add_subplot(111, projection='3d')\n",
+        "ax.quiver(X, Y, Z, U, V, W, length=1)\n",
+        "ax.set_xlim([0, 1])\n",
+        "ax.set_ylim([0, 1])\n",
+        "ax.set_zlim([0, 1])\n",
+        "ax.set_xlabel('X')\n",
+        "ax.set_ylabel('Y')\n",
+        "ax.set_zlabel('Z')\n",
+        "plt.show()"
       ],
-      "execution_count": 0,
-      "outputs": []
+      "execution_count": 17,
+      "outputs": [
+        {
+          "output_type": "display_data",
+          "data": {
+            "image/png": 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\n",
+            "text/plain": [
+              "<Figure size 432x288 with 1 Axes>"
+            ]
+          },
+          "metadata": {
+            "tags": [],
+            "needs_background": "light"
+          }
+        }
+      ]
     },
     {
       "cell_type": "markdown",
@@ -86,18 +176,18 @@
       "metadata": {
         "id": "ah6zMSLJdJwL",
         "colab_type": "code",
-        "outputId": "b1ccb836-02b8-4d42-a7db-6c34f010f6c6",
         "colab": {
           "base_uri": "https://localhost:8080/",
-          "height": 52
-        }
+          "height": 51
+        },
+        "outputId": "1c9b6769-60ef-4687-aa3a-35e02fd58980"
       },
       "source": [
         "from math import e, pi\n",
         "print(e)\n",
         "print(pi)"
       ],
-      "execution_count": 0,
+      "execution_count": 18,
       "outputs": [
         {
           "output_type": "stream",
@@ -114,13 +204,44 @@
       "metadata": {
         "id": "3qpwDlzXkVf5",
         "colab_type": "code",
-        "colab": {}
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 269
+        },
+        "outputId": "6338d6a6-22cb-40d1-f567-803da1eec953"
       },
       "source": [
-        ""
+        "\n",
+        "g = np.multiply(5, p)\n",
+        "\n",
+        "r = np.multiply(math.pi, p)\n",
+        "\n",
+        "o = np.multiply(math.e, p)\n",
+        "\n",
+        "plt.arrow (0,0, r[0], r[1],head_width=.07,head_length=0.05, color='red')\n",
+        "plt.arrow (0,0, g[0], g[1],head_width=.07, head_length=0.05, color='green')\n",
+        "plt.arrow(0,0, p[0], p[1],head_width=.07, head_length=0.05, color ='blue')\n",
+        "plt.arrow (0,0, o[0], o[1],head_width=.07, head_length=0.05, color='orange')\n",
+        "plt.xlim(0,4)\n",
+        "plt.ylim(0,4)\n",
+        "plt.show()"
       ],
-      "execution_count": 0,
-      "outputs": []
+      "execution_count": 116,
+      "outputs": [
+        {
+          "output_type": "display_data",
+          "data": {
+            "image/png": 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\n",
+            "text/plain": [
+              "<Figure size 432x288 with 1 Axes>"
+            ]
+          },
+          "metadata": {
+            "tags": [],
+            "needs_background": "light"
+          }
+        }
+      ]
     },
     {
       "cell_type": "markdown",
@@ -143,13 +264,36 @@
       "metadata": {
         "id": "I1BGXA_skV-b",
         "colab_type": "code",
-        "colab": {}
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 269
+        },
+        "outputId": "84292b37-9d11-4d23-bc68-62cf461c77bf"
       },
       "source": [
-        ""
+        "\n",
+        "plt.arrow(0, 0, 5, 7, head_width=.05, head_length=0.01, color = \"r\")\n",
+        "plt.arrow(0, 0, 3, 4, head_width=.05, head_length=0.01, color = \"b\")\n",
+        "plt.xlim(1,8)\n",
+        "plt.ylim(1,8)\n",
+        "plt.show()"
       ],
-      "execution_count": 0,
-      "outputs": []
+      "execution_count": 117,
+      "outputs": [
+        {
+          "output_type": "display_data",
+          "data": {
+            "image/png": "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\n",
+            "text/plain": [
+              "<Figure size 432x288 with 1 Axes>"
+            ]
+          },
+          "metadata": {
+            "tags": [],
+            "needs_background": "light"
+          }
+        }
+      ]
     },
     {
       "cell_type": "markdown",
@@ -166,13 +310,69 @@
       "metadata": {
         "id": "68sWHIOPkXp5",
         "colab_type": "code",
-        "colab": {}
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 34
+        },
+        "outputId": "477d507d-8f96-4dfc-8388-9a350bbb8db8"
       },
       "source": [
-        ""
+        "a = ([5,7])\n",
+        "b = ([3,4])\n",
+        "\n",
+        "np.subtract(a, b)"
       ],
-      "execution_count": 0,
-      "outputs": []
+      "execution_count": 37,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "array([2, 3])"
+            ]
+          },
+          "metadata": {
+            "tags": []
+          },
+          "execution_count": 37
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "metadata": {
+        "id": "3Eg2rDz2hro6",
+        "colab_type": "code",
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 269
+        },
+        "outputId": "1db2ba79-658c-4ede-b4bb-f9dddcf6fdec"
+      },
+      "source": [
+        "plt.arrow(0, 0, 5, 7, head_width=.05, head_length=0.06, color = \"r\")\n",
+        "plt.arrow(0, 0, 3, 4, head_width=.05, head_length=0.06, color = \"b\")\n",
+        "plt.arrow(0, 0, 2, 3, head_width=.05, head_length=0.06, color = \"g\")\n",
+        "plt.xlim(0,8)\n",
+        "plt.ylim(0,8)\n",
+        "plt.show()"
+      ],
+      "execution_count": 115,
+      "outputs": [
+        {
+          "output_type": "display_data",
+          "data": {
+            "image/png": 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\n",
+            "text/plain": [
+              "<Figure size 432x288 with 1 Axes>"
+            ]
+          },
+          "metadata": {
+            "tags": [],
+            "needs_background": "light"
+          }
+        }
+      ]
     },
     {
       "cell_type": "markdown",
@@ -195,13 +395,33 @@
       "metadata": {
         "id": "2_cZQFCskYNr",
         "colab_type": "code",
-        "colab": {}
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 34
+        },
+        "outputId": "398c165d-aa99-4bd7-a52f-a14209f4d4ed"
       },
       "source": [
-        ""
+        "c = ([7, 22, 4, 16])\n",
+        "d = ([12, 6, 2, 9])\n",
+        "\n",
+        "np.multiply(c, d)"
       ],
-      "execution_count": 0,
-      "outputs": []
+      "execution_count": 39,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "array([ 84, 132,   8, 144])"
+            ]
+          },
+          "metadata": {
+            "tags": []
+          },
+          "execution_count": 39
+        }
+      ]
     },
     {
       "cell_type": "markdown",
@@ -224,13 +444,37 @@
       "metadata": {
         "id": "ku-TdCKAkYs8",
         "colab_type": "code",
-        "colab": {}
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 34
+        },
+        "outputId": "149b7bc8-d81a-4564-9774-ad30bbd75c46"
       },
       "source": [
-        ""
+        "e = ([5,\n",
+        "      7,\n",
+        "      2])\n",
+        "f = ([3,\n",
+        "      4,\n",
+        "      6])\n",
+        "\n",
+        "np.multiply(e, f)"
       ],
-      "execution_count": 0,
-      "outputs": []
+      "execution_count": 40,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "array([15, 28, 12])"
+            ]
+          },
+          "metadata": {
+            "tags": []
+          },
+          "execution_count": 40
+        }
+      ]
     },
     {
       "cell_type": "markdown",
@@ -253,13 +497,48 @@
       "metadata": {
         "id": "-5VKOMKBlgaA",
         "colab_type": "code",
-        "colab": {}
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 269
+        },
+        "outputId": "fda89daf-b2c8-4b41-fb46-1b6e658fec95"
       },
       "source": [
-        ""
+        "g = ([1, 1, 1, 8])\n",
+        "h = ([3, 3, 3, 3])\n",
+        "\n",
+        "plt.arrow(0, 0, 2, 7, head_width=.02, head_length=0.01, color = \"r\")\n",
+        "plt.arrow(0, 0, 6, 6, head_width=.02, head_length=0.01, color = \"b\")\n",
+        "plt.xlim(0,8)\n",
+        "plt.ylim(0,8)\n",
+        "plt.show()"
       ],
-      "execution_count": 0,
-      "outputs": []
+      "execution_count": 114,
+      "outputs": [
+        {
+          "output_type": "display_data",
+          "data": {
+            "image/png": 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\n",
+            "text/plain": [
+              "<Figure size 432x288 with 1 Axes>"
+            ]
+          },
+          "metadata": {
+            "tags": [],
+            "needs_background": "light"
+          }
+        }
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "yw5BnK4rmBDc",
+        "colab_type": "text"
+      },
+      "source": [
+        "**H vector is long than G vector**"
+      ]
     },
     {
       "cell_type": "markdown",
@@ -308,18 +587,200 @@
         "\\end{align}"
       ]
     },
+    {
+      "cell_type": "code",
+      "metadata": {
+        "id": "g2H8ZmBtoYL6",
+        "colab_type": "code",
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 34
+        },
+        "outputId": "1be72357-4cc5-41d7-f11e-91b283261642"
+      },
+      "source": [
+        "a = ([[1, 2],\n",
+        "     [3, 4],\n",
+        "      [5, 6]])\n",
+        "\n",
+        "rows = len(a)\n",
+        "columns = len(a[0])\n",
+        "\n",
+        "print (\"A's dimension is: \", rows, columns)"
+      ],
+      "execution_count": 52,
+      "outputs": [
+        {
+          "output_type": "stream",
+          "text": [
+            "A's dimension is:  3 2\n"
+          ],
+          "name": "stdout"
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "metadata": {
+        "id": "AUt5ZmrtpCd2",
+        "colab_type": "code",
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 34
+        },
+        "outputId": "c9125ee8-dc27-41d4-c928-01e01c5250f0"
+      },
+      "source": [
+        "b = ([2, 4, 6])\n",
+        "\n",
+        "rows = len(b)\n",
+        "\n",
+        "\n",
+        "print (\"B's dimension is: \", rows)"
+      ],
+      "execution_count": 55,
+      "outputs": [
+        {
+          "output_type": "stream",
+          "text": [
+            "B's dimension is:  3\n"
+          ],
+          "name": "stdout"
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "metadata": {
+        "id": "OX7hybnapTVz",
+        "colab_type": "code",
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 34
+        },
+        "outputId": "1ddd793b-bb0e-497e-a260-591cae07fb3d"
+      },
+      "source": [
+        "c = ([[9, 4, 3],\n",
+        "      [4, 7, 11]])\n",
+        "\n",
+        "rows = len(c)\n",
+        "columns = len(c[0])\n",
+        "\n",
+        "print (\"C's dimension is: \", rows, columns)"
+      ],
+      "execution_count": 56,
+      "outputs": [
+        {
+          "output_type": "stream",
+          "text": [
+            "C's dimension is:  2 3\n"
+          ],
+          "name": "stdout"
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "metadata": {
+        "id": "ZEbnmbI9plHG",
+        "colab_type": "code",
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 34
+        },
+        "outputId": "260026e8-3a7e-4d77-f27a-e1bbea4ececd"
+      },
+      "source": [
+        "d = ([[1, 0, 0],\n",
+        "      [0, 1, 0],\n",
+        "      [0, 0, 1]])\n",
+        "\n",
+        "rows = len(d)\n",
+        "columns = len(d[0])\n",
+        "\n",
+        "print (\"D's dimension is: \", rows, columns)"
+      ],
+      "execution_count": 57,
+      "outputs": [
+        {
+          "output_type": "stream",
+          "text": [
+            "D's dimension is:  3 3\n"
+          ],
+          "name": "stdout"
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "metadata": {
+        "id": "UVEALkXVp1X4",
+        "colab_type": "code",
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 34
+        },
+        "outputId": "da713228-5f8e-4ce9-a3bb-b9b99a190820"
+      },
+      "source": [
+        "e = ([[1, 3],\n",
+        "      [5, 7]])\n",
+        "\n",
+        "rows = len(e)\n",
+        "columns = len(e[0])\n",
+        "\n",
+        "print (\"E's dimension is: \", rows, columns)"
+      ],
+      "execution_count": 58,
+      "outputs": [
+        {
+          "output_type": "stream",
+          "text": [
+            "E's dimension is:  2 2\n"
+          ],
+          "name": "stdout"
+        }
+      ]
+    },
     {
       "cell_type": "code",
       "metadata": {
         "id": "Z69c-uPtnbIx",
         "colab_type": "code",
-        "colab": {}
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 68
+        },
+        "outputId": "8b07cf3b-92d9-453f-a973-eacd1ffd3e23"
       },
       "source": [
-        ""
+        "import numpy as np\n",
+        "a = np.array([[1, 2],\n",
+        "     [3, 4],\n",
+        "      [5, 6]])\n",
+        "c = np.array([[9, 4, 3],\n",
+        "              [4, 7, 11]])\n",
+        "\n",
+        "np.matmul(a, c)"
       ],
-      "execution_count": 0,
-      "outputs": []
+      "execution_count": 50,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "array([[17, 18, 25],\n",
+              "       [43, 40, 53],\n",
+              "       [69, 62, 81]])"
+            ]
+          },
+          "metadata": {
+            "tags": []
+          },
+          "execution_count": 50
+        }
+      ]
     },
     {
       "cell_type": "markdown",
@@ -336,13 +797,212 @@
       "metadata": {
         "id": "zhKwiSItoE2F",
         "colab_type": "code",
-        "colab": {}
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 51
+        },
+        "outputId": "a2f79d0d-bf12-4c79-9e8b-ade736b6ffc5"
       },
       "source": [
-        ""
+        "cd= np.matmul(c, d)\n",
+        "\n",
+        "cd"
       ],
-      "execution_count": 0,
-      "outputs": []
+      "execution_count": 64,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "array([[ 9,  4,  3],\n",
+              "       [ 4,  7, 11]])"
+            ]
+          },
+          "metadata": {
+            "tags": []
+          },
+          "execution_count": 64
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "metadata": {
+        "id": "r38kld5arU6J",
+        "colab_type": "code",
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 34
+        },
+        "outputId": "b3f3a26e-6c0f-4647-941b-aca8c3652862"
+      },
+      "source": [
+        "rows = len(cd)\n",
+        "columns = len(cd[0])\n",
+        "\n",
+        "print (\"CD's dimension is: \", rows, columns )"
+      ],
+      "execution_count": 65,
+      "outputs": [
+        {
+          "output_type": "stream",
+          "text": [
+            "CD's dimension is:  2 3\n"
+          ],
+          "name": "stdout"
+        }
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "Tj9ClVcvrAyG",
+        "colab_type": "text"
+      },
+      "source": [
+        "**The new matrices does not relate to D in dimension but it does relate to C in dimension**"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "metadata": {
+        "id": "07g-CdJVqzrD",
+        "colab_type": "code",
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 68
+        },
+        "outputId": "ca099ec0-5779-44c6-b43c-1636dbb1987a"
+      },
+      "source": [
+        "AE = np.matmul(a, e)\n",
+        "\n",
+        "AE"
+      ],
+      "execution_count": 66,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "array([[11, 17],\n",
+              "       [23, 37],\n",
+              "       [35, 57]])"
+            ]
+          },
+          "metadata": {
+            "tags": []
+          },
+          "execution_count": 66
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "metadata": {
+        "id": "tVhjbQjrsMr6",
+        "colab_type": "code",
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 34
+        },
+        "outputId": "a479a25e-079d-4d82-dee0-ae7b0838e6a7"
+      },
+      "source": [
+        "rows = len(AE)\n",
+        "columns = len(AE[0])\n",
+        "\n",
+        "print (\"AE's dimension is: \", rows, columns)"
+      ],
+      "execution_count": 67,
+      "outputs": [
+        {
+          "output_type": "stream",
+          "text": [
+            "AE's dimension is:  3 2\n"
+          ],
+          "name": "stdout"
+        }
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "XAmw1P6JshJn",
+        "colab_type": "text"
+      },
+      "source": [
+        "**The new matrices (AE) does not relate to E dimension but does relate to A dimension**"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "metadata": {
+        "id": "7M4gPzH8q4HO",
+        "colab_type": "code",
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 34
+        },
+        "outputId": "8d4ddc58-1fc8-4737-b800-672183a6594e"
+      },
+      "source": [
+        "BA = np.matmul(b, a)\n",
+        "\n",
+        "BA"
+      ],
+      "execution_count": 68,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "array([44, 56])"
+            ]
+          },
+          "metadata": {
+            "tags": []
+          },
+          "execution_count": 68
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "metadata": {
+        "id": "caqVPdBfs3iA",
+        "colab_type": "code",
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 34
+        },
+        "outputId": "94d9defb-c91c-492f-f5c6-e70476d9cc17"
+      },
+      "source": [
+        "columns = len(BA)\n",
+        "\n",
+        "print (\"BA's dimension is: \", columns)"
+      ],
+      "execution_count": 72,
+      "outputs": [
+        {
+          "output_type": "stream",
+          "text": [
+            "BA's dimension is:  2\n"
+          ],
+          "name": "stdout"
+        }
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "QyWakU60tk0b",
+        "colab_type": "text"
+      },
+      "source": [
+        "**The new matrices (BA) does relate to B dimension by by being one row, and relates to A dimension by having two columns**"
+      ]
     },
     {
       "cell_type": "markdown",
@@ -365,18 +1025,76 @@
         "\\end{align}"
       ]
     },
+    {
+      "cell_type": "code",
+      "metadata": {
+        "id": "BTRHnRuxwIoT",
+        "colab_type": "code",
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 34
+        },
+        "outputId": "17346bff-9db3-4add-d21c-eebcd73b6371"
+      },
+      "source": [
+        "len(F)"
+      ],
+      "execution_count": 77,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "5"
+            ]
+          },
+          "metadata": {
+            "tags": []
+          },
+          "execution_count": 77
+        }
+      ]
+    },
     {
       "cell_type": "code",
       "metadata": {
         "id": "Wl3ElwgLqaAn",
         "colab_type": "code",
-        "colab": {}
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 85
+        },
+        "outputId": "a43bfe5b-1d04-4df8-dd8c-406cb56438ba"
       },
       "source": [
-        ""
+        "F = ([[20, 19, 18, 17],\n",
+        "      [16, 15, 14, 13],\n",
+        "      [12, 11, 10, 9],\n",
+        "      [8, 7, 6, 5],\n",
+        "      [4, 3, 2, 1]])\n",
+        "\n",
+        "FT = np.transpose(F)\n",
+        "\n",
+        "FT"
       ],
-      "execution_count": 0,
-      "outputs": []
+      "execution_count": 76,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "array([[20, 16, 12,  8,  4],\n",
+              "       [19, 15, 11,  7,  3],\n",
+              "       [18, 14, 10,  6,  2],\n",
+              "       [17, 13,  9,  5,  1]])"
+            ]
+          },
+          "metadata": {
+            "tags": []
+          },
+          "execution_count": 76
+        }
+      ]
     },
     {
       "cell_type": "markdown",
@@ -413,13 +1131,36 @@
       "metadata": {
         "id": "ZnqvZBOYqar3",
         "colab_type": "code",
-        "colab": {}
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 51
+        },
+        "outputId": "a835103f-14c2-4cc2-f7f2-5c9200c98ecd"
       },
       "source": [
-        ""
+        "G = np.array([[13, 14],\n",
+        "              [21, 12]])\n",
+        "I =  np.array([[11, 12],\n",
+        "              [23, 13]])\n",
+        "\n",
+        "np.matmul(G, I)"
       ],
-      "execution_count": 0,
-      "outputs": []
+      "execution_count": 73,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "array([[465, 338],\n",
+              "       [507, 408]])"
+            ]
+          },
+          "metadata": {
+            "tags": []
+          },
+          "execution_count": 73
+        }
+      ]
     },
     {
       "cell_type": "markdown",
@@ -456,7 +1197,7 @@
       "source": [
         ""
       ],
-      "execution_count": 0,
+      "execution_count": null,
       "outputs": []
     },
     {
@@ -479,7 +1220,7 @@
       "source": [
         ""
       ],
-      "execution_count": 0,
+      "execution_count": null,
       "outputs": []
     },
     {