LS_DS9_131_Vectors_and_Matrices.ipynb

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        "<a href=\"https://colab.research.google.com/github/nikibhatt/DS-Unit-1-Sprint-1-Data-Wrangling-and-Storytelling/blob/master/LS_DS9_131_Vectors_and_Matrices.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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      "source": [
        "## Objectives:\n",
        "- Student should be able to Explain why we care about linear algebra in the scope of data science\n",
        "- Student should be able to Conceptualize and utilize vectors and matrices through matrix operations and properties such as: square matrix, identity matrix, transpose and inverse"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
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        "id": "P1wyKUbyoFmR"
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      "source": [
        "# Why Linear Algebra? (ELI5 + Soapbox)\n",
        "\n",
        "Data Science, Machine Learning, and Artificial intelligence is all about getting computers to do things for us better, cheaper, and faster than we could do them ourselves.\n",
        "\n",
        "How do we do that? Computers are good at doing small repetitive tasks (like arithmetic). if we tell them what small repetitive tasks to do in the right order then sometimes all of those combined behaviors will result in something that looks like a human's behavior (or at least the decisions/output look like something a human might decide to do/create).\n",
        "\n",
        "<img alt=\"Le Comte de Belamy - GAN Art\" src=\"https://obvious-art.com/assets/img/comtedorures.jpg\" width=\"300\">\n",
        "\n",
        "[Le Comte de Belamy](https://obvious-art.com/le-comte-de-belamy.htm)\n",
        "\n",
        "The set of instructions that we give to a computer to complete certain tasks is called an **algorithm**. The better that we can organize the set of instructions, the faster that computers can do them. The method that we use to organize and store our set of instructions so that the computer can do them super fast is called a **data structure**. The practice of optimizing the organization of our data structures so that they run really fast and efficiently is called **computer science**. (This is why we will have a unit dedicated solely to computer science in a few months). Data Scientists should care how fast computers can process their sets of instructions (algorithms)."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
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        "id": "_3uzRFr5_53h"
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      "source": [
        "## A set of ordered instructions\n",
        "\n",
        "Here's a simple data structure, in Python it's known as a **list**. It's one of the simplest ways that we can store things (data) and maintain their order. When giving instructions to a computer, it's important that the computer knows in what order to execute them."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "XPwuTmmF88Vc",
        "colab": {}
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      "source": [
        "selfDrivingCarInstructions = [\"open door\", \n",
        "          \"sit on seat\", \n",
        "          \"put key in ignition\", \n",
        "          \"turn key to the right until it stops\", \n",
        "          \"push brake pedal\", \n",
        "          \"change gear to 'Drive'\", \n",
        "          \"release brake pedal\", \n",
        "          \"push gas pedal\",\n",
        "          '''turn wheel to navigate streets with thousands of small rules and \n",
        "          exeptions to rules all while avoiding collision with other \n",
        "          objects/humans/cars, obeying traffic laws, not running out of fuel and \n",
        "          getting there in a timely manner''',\n",
        "          \"close door\"]\n",
        "\n",
        "# We'll have self-driving cars next week for sure. NBD"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
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      },
      "source": [
        "# Maintaining the order of our sets of ordered instruction-sets\n",
        "Here's another data structure we can make by putting lists inside of lists, this is called a two-dimensional list. Sometimes it is also known as a two-dimensional array or --if you put some extra methods on it-- a dataframe. As you can see things are starting to get a little bit more complicated."
      ]
    },
    {
      "cell_type": "code",
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        "colab_type": "code",
        "id": "TVxRAWPi_IWE",
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      "source": [
        "holdMyData = [\n",
        "    [1,2,3],\n",
        "    [4,5,6],\n",
        "    [7,8,9]\n",
        "]\n",
        "\n",
        "# Disregard the quality of these bad instructions"
      ],
      "execution_count": 0,
      "outputs": []
    },
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      "cell_type": "markdown",
      "metadata": {
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      "source": [
        "## Linear Algebra - organize and execute big calculations/operations really fast\n",
        "\n",
        "So why linear algebra? Because the mathematical principles behinds **vectors** and **matrices** (lists and 2D lists) will help us understand how we can tell computers how to do an insane number of calculations in a very short amount of time.\n",
        "\n",
        "Remember when we said that computers are really good at doing small and repetitive tasks very quickly?\n",
        "\n",
        "## I Give You... Matrix Multiplication:\n",
        "\n",
        "<img src=\"https://2000thingswpf.files.wordpress.com/2013/04/794-002.png?w=630\" width=\"400\">\n",
        "\n",
        "If you mess up any of those multiplications or additions you're up a creek.\n",
        "\n",
        "## I Give You... Finding the Determinant of a Matrix: (an introductory linear algebra topic)\n",
        "\n",
        "## 2x2 Matrix\n",
        "\n",
        "<img src=\"http://cdn.virtualnerd.com/tutorials/Alg2_04_01_0017/assets/Alg2_04_01_0017_D_01_16.png\" width=\"400\">\n",
        "Just use the formula!</center>\n",
        "\n",
        "## 3x3 Matrix\n",
        "\n",
        "<img src=\"https://www.thecalculator.co/includes/forms/assets/img/Matrix%20determinant%203x3%20formula.jpg\" width='400'>\n",
        "Just calculate the determinant of 3 different 2x2 matrices and multiply them by 3 other numbers and add it all up.\n",
        "     \n",
        "## 4x4 Matrix\n",
        "\n",
        "<img src=\"https://semath.info/img/inverse_cofactor_ex4_02.jpg\" width='400'>\n",
        "Just calculate 3 diferent 3x3 matrix determinants which will require the calculating of 9 different 2x2 matrix determinants, multiply them all by the right numbers and add them all up. And if you mess up any of those multiplications or additions you're up a creek.\n",
        "\n",
        "## 5x5 Matrix! \n",
        "\n",
        "\n",
        "## ...\n",
        "\n",
        "\n",
        "## ...\n",
        "\n",
        "Just kidding, any linear algebra professor who assigns the hand calculation of a 5x5 matrix determinant (or larger) is a sadist. This is what computers were invented for! Why risk so much hand calculation in order to do something that computers **never** make a mistake at?\n",
        "\n",
        "By the way, when was the last time that you worked with a dataframe that was 4 rows x 4 columns or smaller?\n",
        "\n",
        "Quick, find the determinant of this 42837x42837 dataframe by hand!"
      ]
    },
    {
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      "source": [
        "# Common Applications of Linear Algebra in Data Science:\n",
        "\n",
        "- Vectors: Rows, Columns, lists, arrays\n",
        "\n",
        "- Matrices: tables, spreadsheets, dataframes\n",
        "\n",
        "- Linear Regression: (You might remember from the intro course)\n",
        "\n",
        "<img src=\"https://jeffycyang.github.io/content/images/2015/11/Screen-Shot-2015-11-28-at-7-35-39-PM.png\" width=\"400\">"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
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        "outputId": "e4a5b0c0-972c-45ed-ef65-e313c3ff5ef6",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        }
      },
      "source": [
        "# Linear Regression Example\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "\n",
        "# Read CSV\n",
        "df = pd.read_csv('https://raw.githubusercontent.com/ryanleeallred/datasets/master/Ice_Cream_Sales.csv')\n",
        "\n",
        "# Create Column of 1s\n",
        "df['Ones'] = np.ones(11)\n",
        "\n",
        "# Format X and Y Matrices\n",
        "X = df[['Ones', 'Farenheit']].as_matrix()\n",
        "Y = df['Dollars'].as_matrix().reshape(-1, 1)\n",
        "\n",
        "# Calculate Beta Values\n",
        "beta = np.matmul(np.linalg.inv(np.matmul(np.transpose(X), X)), np.matmul(np.transpose(X), Y))\n",
        "\n",
        "print(beta)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[-596.20648399]\n",
            " [  24.68849397]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
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      "source": [
        "# Assign Beta Values to Variables\n",
        "beta_0 = beta[0,0]\n",
        "beta_1 = beta[1,0]\n",
        "\n",
        "# Plot points with line of best fit\n",
        "plt.scatter(df['Farenheit'], df['Dollars'])\n",
        "axes = plt.gca()\n",
        "x_vals = np.array(axes.get_xlim())\n",
        "y_vals = beta_0 + beta_1 * x_vals\n",
        "plt.plot(x_vals, y_vals, '-', color='b')\n",
        "plt.title('Ice Cream Sales Regression Line')\n",
        "plt.xlabel('Farenheit')\n",
        "plt.ylabel('Dollars')\n",
        "plt.show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
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Xftll6tpF5Owp4EVCQFqaiSFDHPzrXzYiIgzGjXPx2GPq2kXk3Cng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\nAAAASUVORK5CYII=\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f4041067da0>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "_ESowKHqcXfy"
      },
      "source": [
        "- Dimensionality Reduction Techniques: Principle Component Analysis (PCA) and Singular Value Decomposition (SVD)\n",
        "\n",
        "Take a giant dataset and distill it down to its important parts. (typically as a pre-processing step for creating visualizations or putting into other models.)\n",
        "\n",
        "<img src=\"http://www.sthda.com/english/sthda-upload/figures/principal-component-methods/006-principal-component-analysis-scatter-plot-data-mining-1.png\" width=\"400\">"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "Egs4F1Wgcb3J"
      },
      "source": [
        "- Deep Learning: Convolutional Neural Networks, (Image Recognition)\n",
        "\n",
        "\n",
        "\n",
        "\"Convolving\" is the process of passing a filter/kernel (small matrix) over the pixels of an image, multiplying them together, and using the result to create a new matrix. The resulting matrix will be a new image that has been modified by the filter to emphasize certain qualities of an image. This is entirely a linear algebra-based process. A convolutional neural network learns the filters that help it best identify certain aspects of images and thereby classify immages more accurately. \n",
        "\n",
        "<img src=\"https://icecreamlabs.com/wp-content/uploads/2018/08/33-con.gif\">"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "2P8WEcCagBBx",
        "outputId": "280f6413-98c3-4ee0-b072-77aded5fa1c0",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 87
        }
      },
      "source": [
        "!pip install imageio"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Requirement already satisfied: imageio in /usr/local/lib/python3.6/dist-packages (2.4.1)\n",
            "Requirement already satisfied: numpy in /usr/local/lib/python3.6/dist-packages (from imageio) (1.14.6)\n",
            "Requirement already satisfied: pillow in /usr/local/lib/python3.6/dist-packages (from imageio) (4.0.0)\n",
            "Requirement already satisfied: olefile in /usr/local/lib/python3.6/dist-packages (from pillow->imageio) (0.46)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "5zVI4VWxknx-",
        "outputId": "b0223466-fa2f-4c3a-a76c-3a9932c6323e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 269
        }
      },
      "source": [
        "# Convolution in action\n",
        "import imageio\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "import scipy.ndimage as nd\n",
        "from skimage.exposure import rescale_intensity\n",
        "from skimage import color\n",
        "\n",
        "img = imageio.imread('https://www.dropbox.com/s/dv3vtiqy439pzag/all_the_things.png?raw=1')\n",
        "plt.axis('off')\n",
        "plt.imshow(img);"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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IO1QWgbpii4pjopgIZrnVZROXEV0iN/QBZBNPz5DSi8ztcTwMBLmN8+fPszTp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\n85dv59x3ncFrzj4BY4UiTTE2WNXYaMetdNe3VmMUJUdljKnThVNefAg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9lpdc+DqsEnTQ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\ndcndbwAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "DjvrPkWVlH11",
        "outputId": "e0053a8d-0be9-4635-efc0-b951c493df70",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 269
        }
      },
      "source": [
        "# Convert I to grayscale, so it will be MxNx1 instead of MxNx4\n",
        "grayscale = color.rgb2gray(img)\n",
        "plt.axis('off')\n",
        "plt.imshow(grayscale, cmap=plt.cm.gray);"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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S02rHIstOJAIRA7WJfnPPPh1D+ill5snWml74Ft0DERTJHnybeGovvUZkfSqL8XTA42+5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\ndisCAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "oX_-JddjlJ9u",
        "outputId": "14e52a74-b494-488e-9035-c8e74c6a4a87",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 269
        }
      },
      "source": [
        "laplacian = np.array([[0,0,1,0,0],\n",
        "              [0,0,2,0,0],\n",
        "              [1,2,-16,2,1],\n",
        "              [0,0,2,0,0],\n",
        "              [0,0,1,0,0]])\n",
        "\n",
        "\n",
        "laplacian_image = nd.convolve(grayscale, laplacian)\n",
        "plt.axis('off')\n",
        "plt.imshow(laplacian_image, cmap=plt.cm.gray);"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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H6DN0/EL1ODiORuvkkwZvD907uXqePPnxKns6nQ7RaFRMqLJWnkwmYbfbYbVa0dnZCZPJ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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "zTp35yHxcx8M",
        "outputId": "864e6873-800f-49ac-887b-8521cc1eda28",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 269
        }
      },
      "source": [
        "sobel_x = np.array([\n",
        "    [-1,0,1],\n",
        "    [-2,0,2],\n",
        "    [-1,0,1]\n",
        "])\n",
        "\n",
        "sobel_x_image = nd.convolve(grayscale, sobel_x)\n",
        "plt.axis('off')\n",
        "plt.imshow(sobel_x_image, cmap=plt.cm.gray);"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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VlB1KKL9PJMVJWJmCrCTRfO6XyolmI/RUKoWqqio4nU6Mj4+vWjlsljRpIqV6FnzFs5Wa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\ngg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "1klzU7gucyEb",
        "outputId": "155d4580-9043-44d9-af43-acaa0e6321b9",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 269
        }
      },
      "source": [
        "sobel_y = np.array([\n",
        "    [1,2,1],\n",
        "    [0,0,0],\n",
        "    [-1,-2,-1]\n",
        "])\n",
        "\n",
        "sobel_y_image = nd.convolve(grayscale, sobel_y)\n",
        "plt.axis('off')\n",
        "plt.imshow(sobel_y_image, cmap=plt.cm.gray);"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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5qSKBNEoHmozXGNxJR1NWi8UiSJBy6wJLO7/dbhednELjuLUlk8dyOhMPASOP\nfylZRkZ14fcYDAbh8/lw+vRplJeXo7KyEn/+53+O1tZWHDp0SDgBf/jDHyIUCgmylJ+5KgyMrqWy\nIGVnq91uR0tLC0KhEFKpFBYWFjA3N4fDhw+Lc1W7jiSTSfh8PgwNDWHXrl3w+/1i52d616prkyOR\n2oTRgE2Qcz7LoW78HE3IpQO9B94aQm7oZO3Qj81mW7JzBIfJtBiTbLfbYbfbAWDJ7hX5LOJ8kMO/\njOpwP6GKjuAEmU6nsbCwgIsXLyIYDKKxsRHHjx/H/v37cefOHZw/fx59fX05O2EQgQHGm3HK0S3y\n//zZA/csY9Kbq6urAQCxWEwQoeoawGIIHbBI1hcvXsTY2NiS+5RB+ZopRWi+8o3qLv/Nz9EoDWjL\neA0hdwQCkbHVahXB92Q1805IFhKw2FlpsQKPEaVpsNx58zllVATMOy+XBtaTpPM5nfj98IgP+t5m\ns2F2dhYzMzP47d/+bfz6r/86stksrl+/jnPnziEQCCzZ/YMkIJIBeOpIKp/nPuazB1nj5xEKdJ2m\npibxd3l5OX7yk5/g0UcfRWNjI1wuV87KwGg0it7eXpSVleFDH/oQXnjhBfzLv/wLrl+/DqvVioaG\nhpyczXTvJGs0NzcDgDLtpcppZ2QNa5QuNBmvE2SCARYJwmq1LtmvjY4jYuAOQILs5COo9GLV5/L3\n/P+N6qwyUfDPaCDicdpEitlsFsFgEAMDA6ioqMCjjz6K0dFR3LlzB/Pz80tiuLkezomYrk2LIGTy\nB4BQKIRYLCbKo1A4s9mMZDKJ2tpauFwuZLNZ1NTUoKmpCWfOnEF9fT3q6+tx9uxZtLW1Yf/+/XC7\n3QAgwuvGx8fx13/91zh58iQA4NSpU7BarfB6vairqxPvX353FotFRFNwyYU/Q1Wb4W1L9dw1SZcW\nNBmvMeRpISdX4J6mbLPZhMOOL5vl5/K8tSRbkPON68mqKSq/JhETt/ZIS+XhZHJd1wsqK55Wl/n9\nfvT19aG/v18kVHc6nfB4PDhy5AhOnDiBeDyOy5cv501+xAclm82Wcyy/z1gshtnZWUxMTODSpUsA\nIHIhk7REDlir1YpgMIh0Oo0PfvCDGBkZwfHjx/GRj3wEt27dgsViwfT0NAYGBvDqq68KK7apqQlH\njhzBv//7vyMYDOL999/HnTt38Nhjj+HFF1/Et771LUQiEUHe/Pk4nU6Ul5cjEAiIaA7Ve+LEKy+V\nzvd8NEoHmow3AEaRAg6HQ+iPfGpM4NsBEcrKygRR07k8Ptlok0n+mSxJGG0LtFHIZrMIh8N4++23\n4ff7cfz4cfzt3/4t2tvbkU6tUuogAAAgAElEQVSnMTo6ijfffBN2ux0jIyO4ffu20GYLySr83ki6\nyGQymJqawuDgIK5du4ZDhw5h3759ePLJJ7F9+3Z0d3ejvr4ePp8PDodDRD3Y7XaEQiH09fXh7//+\n7zE8PIxMJoOZmRns3bsXX/ziF+Hz+TA5OQmv1wu3242mpiY0NjYiFArh9ddfx8TEBIBFwr958yba\n2trw9NNP480330RLSwsaGxtziDWRSCAej6OlpUVEiKjkMD4L26hBVWNtocl4A6DS76jD0NQ031JY\nfj63bOWOJ8sedK7Ki853AaGy+bU2Aly+uXbtGkwmE5599ll88YtfFMnXgcWlyVu3bsW3vvUtnDt3\nDhUVFThy5MiS+qoIiD8XkocGBwdx+vRpJBIJPPfcc/h//+//oa6uDlevXkUoFEIymcTdu3dRUVEh\nyH/Lli0IhULw+XxwuVzYu3cvbt26Ba/Xi4mJCdy9excmkwkHDx5EfX19znu4dOkSrl69iunp6ZyB\nN5VKiVjndDoNr9eL+vr6nPdFvgaHw5GzM4dKrlrucnqN0oJeDq2ATIKUP4AnfyEU0+iNnCokMZC1\nRrJFPmuPSxJUJlnIwFIHn9H9cWmCdFF5irse4O2N7nlmZgY+nw9/8id/grq6Opw9e1Zss0TPqKmp\nCSdOnMDU1BT+8R//EW1tbWhoaBAShOpeefRINBrFG2+8gbGxMbS2tuJrX/sadu/ejbm5OZw7dw7J\nZBINDQ0YHx9HNBqF3W6H3+9HOBxGU1MTxsfHxQAWDAaxZcsWxGIxvPfeezhx4oRI5GOxWES+DZ7F\nj1YV8sgOes/79+9HX18f3n//fbS3t4tUnvRO6BlkMhklIZODE9DLnksBejn0GkK2MoksnU6nyFVL\nHa6YwUw+hghPXj7tcDhyCFkVlqS6HpEAWVvAPRLjnZnuTbaaiSgAGIZmrRX4HmxWq1Uk5/md3/kd\nBAIB9Pb2IhQK5ZxDq9h8Ph+2b9+Oz372s/jOd74Ds9mMLVu2AEBOdApPEhQIBPDKK68glUrhxRdf\nxF/8xV/gpZdeQm9vL86dO4eBgQH8+Mc/hsPhQCwWg8fjwdDQEObn51FVVQWbzYZAIIDGxkYxaO3f\nvx+VlZXweDw4dOgQZmdn0drairKyMqTTaUSj0SXPkVvEBHrXg4OD2LZtGwDg+vXraGtrQ3l5ucge\n197eLmLDbTZbjv4vtxXtmNu80GSsAJcPksmkWIxBuQzMZjPi8biIjFgujCxWWfcr5hwgl3i5BUWw\nWq3KhSPyeRsB2dGUzWZRV1eHbDaLGzduKBc20IDi9/tx8+ZNdHZ2orq6ekl6UjovlUrBbrcjEong\nRz/6ERobG7F3716cOnUKBw8exPDwMPr6+sReesPDw0gkEti5cye2bt2KaDSKVCqFXbt2iaTxlZWV\nqK2tFVENVM+KigqMjY2J2HAu/ajunYNkk0gkAqfTiaamJgwMDIj/TSYTysvLhdWrSoHJn5HRdTQ2\nBzQZK2AymcRW6//7v/+L4eFhbNmyBS+88ELOFjjAPQljJVBpvDwxuWo/PVUZ3Cq0WCxixR/JF4lE\nQsQZy9Ne0lJVq7/WAzIZl5WVobGxEQsLCwiHw1hYWBDbLxHBkjREVmcymURTUxP8fr8gPhocU6kU\nRkZG8OabbyIej+NTn/oUvvzlL6OtrQ03b97E6dOnMT4+jrt376Kvrw8LCwv4/d//fUGmJpMJHR0d\nOTJDY2OjqAvlriALtby8HC6XC9PT02hpaSk6TpusWyLk0dFReDwemM1mzMzMoLa2VuwqHY1Gc7ab\nkldQyo47jc0JTcYKUCexWq3o7OzEwsICRkZG8J//+Z84fPgwmpqalIlhlgtZhuBl5pMlCpUF3Nv6\nicrjVhXPq6BK0r6e4MRhNptRVlYmokp8Ph9GRkYwMzODtra2HKcU3U8mk0E4HEZlZWXOoOJ0OuHz\n+XDnzh288cYb6Orqwgc/+EF84QtfwNjYGN566y1kMhlcv34dN2/exOTkJObn53Ho0CGx3JgGQIop\nJvmG+wmIlGmgczqdqKurQzweRzAYRHV1ddF+BBoAST92u91oaGhAPB4Xclg8HhcRNLJmzKGjKDY/\nHnoHHr9/bp1SZ2tqagKwuNpqYmIC3//+9zE2Ngan04ldu3Zhz549OXljOblxy0UF1dSSzqd8yICx\njsslBpm8eafkVjC3nnjMM08ss56Q2xtfcVZdXY0tW7agoaEBZ86cyUmcxEmLZz+j99Tb24upqSkc\nO3YML730Eu7evYuWlhbMzs5icHAQkUgEIyMjCAQCiMViaGtrQ11dHVwuV877UiVPopVx/BlxzZYW\nbty5cwfd3d1Fyz6yRESW8M2bN0UiIQprSyaTiMfjwiKmd6oabGWfh+q5rwRrRfKquhSqn5GDlv+W\ntXP6XagfrjW0A2+FUL0gmur29fVh+/bt2Lt3L4LBIJ599lm8/PLLWFhYwL/927+ht7cXAwMD2LNn\nDwB1KFo+5GuUXAOVs3nJx6vKkYle1ozJ0qTy5Vy66wEuUdDfHo8HU1NTmJqaQkdHB8LhMPr7+4Uc\nwGG1WpFOp3Hnzh20tbWhqqoK586dw61bt/Dxj38cn/vc5zA3N4e5uTnEYjH893//N8rLy/Huu+9i\ndHQUHR0dOHjwIFpaWpZFTvJgSLIOv6/q6mohtZCEVczz4PXw+/3weDxob2/HtWvXUF1djbKyMvh8\nvpxnRtIGj4BROXv5OUaacj5DYb0MNdU15c84mQLqdi63aaN73SwzhYeejDk4Eba0tMBisWBkZAQd\nHR2Ix+M4ffo0tm3bhrq6Ouzfvx+RSASXLl1CW1sbXC7XkjwHhJU2Bt6ZVtuoVA1VjrC4H422rKwM\nlZWVmJqaEqvwuPORWz18xSBFOni9XmzduhWHDh3C2bNnMTU1hXg8jrGxMfT19eHu3buoqanBE088\ngebmZlRWVq4pyRA5AovtJhgMijC35SKdTiMej4vwuGg0CmDxGZFkQ4MnXbsQaRZDfCrIBsVGEnO+\nKCKjvqB6LnIZpU7KmoyxtKGlUinEYjF0dXXh7/7u7+ByuTA2NobXX38dN27cEEnNd+zYAQB4++23\n0djYiEOHDuV0TFkWWI6lTJ2cJIu10AONvPA8Yfp6gnds+ttisaCzsxM9PT24desWWlpaRO4Hfg4R\nFWU5Ky8vx7Vr19DR0YGmpiacP38eVqsVPp8PZ86cwe7du/HYY4+JsLSysrIl1uxagIcTNjY2YnR0\nFE6nEzU1NSsqb3p6GplMBnV1dQgEArDb7aipqYHX682xhoHCRGlkECwn8mIt24SqHxiVbySXyREl\nJFXxfsZlt1InYI6HQjPm95jJLG57ThYWbX1D36VSKYRCISwsLKCyslJsOglAOJAoo1praytOnDiB\nV155BefOncPCwgKOHj0Kt9sttt1ZjcXJ89KudrmyqmPK1sZqyl8JTKbFXL20uu1f//VfYbVaceTI\nEeFUo2m43+/HhQsXYLPZ8Ad/8Af4+c9/Dq/Xi09/+tPYu3cv+vr68JOf/ATDw8Nob2/HI488IiIe\n6F65trqW98l1/qmpKTgcDpFWU77fQrDb7XA4HLh9+zbcbrdw3nESpnbFI29Wek+FJK77BbleRLbU\nF/j3lFSKO6Tv5+IXrRkXAfJOv//++/D7/bBardi1axdqa2sBLG78ODMzg/HxcdTX16O1tRV1dXVi\nWxzKA0FT5vHxcQwMDODpp5+Gx+PB17/+dVy6dAnt7e0iPIoWhxQDvksI1Ze0XZ61bSXkqZrOGllL\nGwWTaXEfuqmpKezZswcHDx7ElStXcPHiRTzyyCNwuVwAFrddunLlCpxOJx5//HExID7yyCOorq5G\nIBCA1+vF7t27sW3bNkFSfJsiemecxNYK3FpzOp0i65usjxfzjM1mM+x2O8rKysQMjXaCIVKWp/Gq\nBUJG1yrkPMsnG6yHA081W1IdSxFAPLqGIl9ooKK+xlc6ytcrZTwUZMxfjM1mQ1VVFdrb25HJZHDm\nzBkkEglhKbe2tuKZZ57BkSNH4HA4MDIygnA4LM7nUQ7JZBIXLlzArl27cPLkSRw8eBBf//rXMTU1\nhcbGRlRVVS2rAfPYYgJZA+S84kl+litdFNNBN5KU6V58Ph/Gxsbw+c9/Hj6fD9/97nfx1ltvwev1\nwmw2o7q6Gr/yK7+Cl19+GWazGd/+9rexa9cu7Nu3D6lUCj09Pbh58ybGxsbQ0NAgBkJuTQLrl6uZ\nv4dUKoVIJCKcfEQgRo5WGUQuTqdTLP5oa2vD7OwsstmsSKFptF8er5MKfFCWLWz5XFkOWSlUVq6q\nLqq/ycKlumYymZzNWYF7DlX6Pl82v1LGQyFTEEymxRVNNTU16O/vx65du3D48GH09PTA6/Xi2LFj\n6OjogM/ng9/vRyAQwPvvvy8WdhSyKnbu3Il0Oo3r16/j4sWLOHDgAOx2+4qcOdTYyPLh+Xm5V/1B\nQmVlJRobG7F//37Mzc1hbGwM27Ztw9atWxEMBtHT04Pp6WmEQiF84AMfQDKZxP/8z//g/fffx9DQ\nEI4ePYqWlhZUV1ffFy866ZcLCwuw2+2oqqoS7w8ozmeQzWZF+s7p6WlUVlbC6XTmLNCRrWEjolc5\n+OSBt9j+v9pnqboWr7e8ahSAaPc8rJBrxGQNU3QJ+VZUURZrcQ/FQssURSCTySAWi6Gmpgbj4+O4\nc+cODh8+jOeffx6RSAQ+nw8DAwO4dOkSgsFgTkYzWR6gzkF5ic1mM0ZHR7Fr1y50dHTg5z//uUhK\nsxIyVjUgkiw268ifDxaLRWRF8/l8aGxsRDQaxdWrVzE3N4fZ2VlMT08DWHz2N27cEItGtm7dirq6\nOmzfvl0Q2Ubp4JwY6f2Qj0EeMAu9M6570rJ7Iha+wwiVJZPNcuoslyHXY62fWSErnmZ99Ax4ilRu\nmMgGCqDemqyY65YaHljLWDX1pkbW1dWF8vJyvPPOOxgcHMTJkydRU1ODWCyGSCSCWCwGAHmdPbzB\nco//zp070dXVheHhYXz729+G0+lEd3d3zsgOFJ4yy0QiZ3gjqaSQR70UnTFGdeI6YHl5ObLZxTzH\nNCMgvd7tduP111/HzMwMGhoa0NjYiK6uLqUksVHtmwiCoj5ooCCZqdj3QKROBFNRUZGzaamR5Wdk\nedJv/jdPVCWDbw/Gr6MKG1OFlxW6N7oGlUmf2e32JX1E7gOcrEkfJokRyJXujHTpjYC2jIsAvaTx\n8XE89dRTePTRRzEyMoJoNIqpqamcqS2XBqihy42XdwxgUY8eHh5GPB5HZ2cnOjs7MTo6ioWFBXg8\nnmWF23BrgK5Fmhh9r9rRoRTIV0a+Osnf0XTT7/cDgBgYy8vLASw+40ceeQT9/f2Yn5/HtWvXkEgk\n0NHRkRPnrdo9Zb1AzjoiTIfDIQbN5UZvENnxsEY5Q5tKg1a1TVkG4J/TwCfns+Z1kFGsxMH7kVxH\n1cAsa+CyZcvrTM+GZA3+bIzC4ZYjx9xPPLCWsRGi0Si+973vIZlM4sCBA2hra0NFRQXKy8vXZGpL\nDYYWh7z77rv47ne/i+rqahw5cgQulytnikXgDY6XI2ufPOFPMpnMIZ3N6EFWgbR9p9OJa9euIR6P\no6OjQ3zf1dWFffv2YXx8HFevXgVQeOq9kchms5idnRWJ4olUi9H4SUqLx+OoqalRhq/JRMs/4w4s\nIjqqg8qpKRMdhQPSoMiNE358sVKAXC8AQorJJ+Fwa5gGIb70ezUyzXpDW8ZFIJvNoqysDJ/73Ofw\ngQ98ACaTCbdu3cLw8LA4Zi08x5lMBoODgygvL8cLL7yAuro6nDlzBjdv3hQ7VKhgNO3jjY2mr7RJ\nJTk0HiQdme7F4XCgubkZg4ODiEajItRtYmICFotFpLy8desWbty4sSFLuotBNptFbW1tTupLSsNa\nCMFgENPT02hqaoLNZoPb7UY0GhUzBAKRG3/vRLaUypPXh75XzbY4MfLIIn5uvrrLz5vLENxapXrR\nrE42NHh9+SBBJJxvQHgQsP5zuBICOQaSySTC4TDq6urw+OOPo6KiQoQgrbYz82nhyMgIJiYmxMaT\nkUgEfr/f0GnCr5+voZFmzBs6P+9BaKRkHbpcLjidTiSTSaRSKTEbGBkZwXvvvYdsNov29nY4HA4A\npSHTkPefwiALhaFxULY4p9OJVCqFcDgsYsyBe4M9f//kOKQfnvmPEyN3dMk/PPmRqh0ZncfP53/z\nZe20bZS8m4xKypANENlRJ9/Dg4SHTqbg3lnS9yhdIcX5ruaZ8NGbrtPZ2Ymuri788pe/xNmzZ7Fl\nyxaxQotPIQnFTAO5nMGXM8tyx2YFTU3tdjsCgQAmJiawfft20Znpt9PpRGdnJ3bu3Ilz584hGAyK\nHBb8HWwkMpkMJicnRRrQQvo1H8CHh4dhsVjQ1dUljAe+I7gsK9AgzssopFNzS5mcojw/sqoN5ZMR\n+H3z7b/kVYOq842sdlnKIH24FPiqELRMUSRoxA6Hw3C5XDmrdVZLxIB6lB8YGMD4+Dj27NmD4eFh\nEQonn8cdEbFYLGcaSTDyZNMgI2uCmxUmkwmxWAxerxcWiwW1tbU5MgQ922QyiVu3bonNRePxOM6e\nPYuZmZmcjryRMJvNcDqd8Hq9wnGrci5xIspkMohGo2JHaY/HI/YG5D4NOp6/Yzmxkvy9qj3wQZzi\nduXv5f9lvZoMGBoAaEZAy5P5Pcp/cyucvuPtnZ5Zvhj/Bw0PPBnzEZ5rUMFgECaTCZWVlTnHrsX1\n+LWy2XubRSYSCbjdbszMzIgQIjqOWzNkEfIOXCgqQCapzU7IFotFJJ6nAYrHWNNnwOK9Tk5OYmho\nCM3Nzdi5cyfC4TAikciSpbEbBafTmePtLwSyUilDWzqdFk5MTpayJakqh3+usm65BkshksVAJU8Q\nKDmPTK5y3eg7btnL+jB37BWa2TwIs0DCA0vGqhdIFktbWxuGh4cxPT2Nqqqqda0HTQGTySRmZ2dR\nW1uL8fFxBINBeDweALkbkwKLnaW8vFxobzymWGUZywRMRLWZG2kqlUJ5eTm2b9+OYDCIixcvwmq1\nigRC1PFpep1IJNDT0wOr1YpDhw5h165dGB8fFwPfRqOyslK8U3llGIHeJ1mVRL7ZbFZsymqz2WCz\n2YRUQeflIyjVwC2To8l0b7cS2ULl58ifySvlKCaZGxRGkNsuL4tb1QByNhaQ6/MgGR0cD6wDT6XF\nZjIZRCIRuN1uHDp0CIFAANeuXVO+9NU6CHiDI2vX5/Nhz549OHbsGIaHh3MsJ1n/i8ViwhqU41ap\nEcvhR9xxspkbKZFTLBaD3+9HTU0NEokErl27hpmZGUEklPiHzkkmk4jFYnj33XdhtVrx+OOPo7Gx\n8b7cQzabzXkXqrA2Imrg3v5+8XhcbPUUi8UwOjoKr9e7ZIZX6Noq5xoA4eikhSTy8UZlJJNJcQ5F\nbJSVlYlBkQabQr4P+Vq0YpGyJ6ZSKZFVkequiqF+EPHAWsbAUicBWQzz8/PYt28ffD4f3nvvvRzH\nnay1rWQE5tflDj3qcE1NTYjH44jFYjlEK1s0fK862SqWQ4Nk3ft+OK7WCjx16MLCAmw2G3bs2IH+\n/n7Mzs6ipaVlieOKx6ECELuF7Nq1C6FQCJFIJCdGdS2tZa7ry/KJEZHw9kQbxtIsiFbd0So4/j5V\nGdqMIEtmJIupnIFGBgnXg4HcXU54G8znLJSP4Xk2OJmriNdIJy/m/jcbHmgyll8UvezR0VFUV1fj\nySefxMjIiEhTaLPZlGE3y7Uy5WkdcG9b9rt376KtrQ2HDh2C1+sVcoSqvvza1AlIP5T3YyMUaz2V\nMoh0rFYrgsEgMpkMdu3ahdnZWYyNjcHv96OysnLJrAC458xaWFhAIBDAkSNHcPToUfT19WFqakpI\nG2uVZIlIhULNqqur0dbWhng8joGBAaFzE+GoHGPl5eVi4C0rK8vJZeLxeBCJRADca0PFOOd4/ehc\nIHcVnMphzWdfdAy9CzlPBL+WkX7N44r5Ag4iYd728w2Qm7k9F4sHVqZQgVtTQ0NDmJqagsvlgtfr\nhcPhUOa7Xe10n86nTjQ/P4/h4WG43W7U1taK6+ULe1LFgBqFLxVrNZU6SIqheF2LxYKKigpks1l4\nvV4Aam2Uv79kMomrV68imUyis7MTdrt9iYNotSBCoevW1NRg586d6O7uzpGRjCxPCl2j3aV5ykiK\nGSZHZLFRIXIbIJlElrq45SxbwgCE5SrnqTBqV/kcdtyK5vHQcpmbWV5bLR4qMqYGYbPZEIvFEIvF\n8OSTT4odhElPW2uHj0pieOSRR3DhwgUMDQ0JfVEF3pC5/kgdnR8n/2zmhk0ERhpif38/duzYIUgO\nyH1PnEz4XnmRSARXrlxBNptFW1vbutSTJz6/cOECvvzlL+NLX/qSkKBUjjAi73Q6LSIvaPABIBa5\nkHNsOZEZdC3uHKMFKKq4YHpmtPrOZrPB4XAIa7gYIqZ7kuvAF5sQsZNcImdbk5/Rw4aHioypYVFm\nrcnJSVRUVKCtrQ2Tk5NIJBLr4vzi07V0Oo1AIACr1YqTJ09ibm5OhHEZnScnhiEHCrBUt1M5Ljcj\nSMcnIvD7/QiHw2hsbITJZEIgEMg5nssVRGBEBsFgEL29vYjH4yJ0bK3A42uz2SwOHDiAP/zDP8Sf\n/umfLtmbTbaQyVqNxWLw+XzIZDJiyTCXJCwWC2KxWFF+AHkmxVfj0bn0fTKZRDweF1nmHA4HysvL\nBQnTsTKJF4LKyi4rK4PT6YTVakUymRQrKTfTYo71xgOtGatgMplgt9uFVzibzWLnzp2IRCKIRqMi\n7SE1YGosPIZyudcDkFMmAIyMjMDlcmHXrl2iwRstBKG/ZQ2ZGjPvbDIRb1ZHHnda8qk1xeLSMwNy\nkyTRs5DJxGQyiTA3GpDXAvKKTgqf5O+FT/v5uyGypgUflESeJwWy2+1wu93i/RrJWbLFC0AsQea5\nS2RNmJO/kf6bzznH3xEdy9scT3fJ65GvLz2sksVDZRkDiy86Ho8jnU4jkUjg8uXL2Lp1K3bu3Il3\n3nkH4+Pj4jhq/CRfrPR69MNXKwWDQYTDYbEbhFECetXUkMqy2Wxi41PSH2Xy3YxEDCyd4gKLUTAO\nhwP79u3D2bNncfbs2YKeedJJ0+k0amtrUVVVlZPrYS3qSQRUXl6O6upq9Pb24hvf+IaQS4wWQ5DV\nGggEkM1mUV1dLaxSqn88HofVaoXX60U0GjV8nzwnBVm42WxWhKPRwE0DGCWaop0ygFzZQjXjMiJp\nLp/w8EoKywTurXylcvNJHg/CzG4leOjIWEYms7j0+Pnnn8fBgwcxPDyMaDQqRnG+j9lagm+7ThuO\nqhwqMmTrxmw2CyLfyBy+9wOJRAITExOoqqrCk08+ierqaoyNjeUkEFJFB5DjLhaLCUlhLUFEQ3se\n1tXV4Y/+6I+Eo0o12GazWSETjI+PiyXQFGfMrf3KykpYrVaxF6OqXcgOOZ6fgwgylUqJbcC4lCO3\nNZXkpSJI2Z9B5fAYZE7CnOQLtXVNxg8hstkspqen4fV60dnZibKyMvT394spJrca1hKJREKQPgX5\n5/O6y/9zUub5AFSOvM1qHXOYTCZEo1H4/X44nU5s2bIF27ZtE5+RZShHSpCVmUqlMDY2hhs3bqz5\n87BaraipqUFDQwNu376Nubk59PX1wWQyiSxsqvdgNptFO6iqqhJbRnGi4jILOfVUGitJJHx2FI/H\nxSBPiyu4BVtIr1WFyMnfy3HAKiedioBVZT4IM7rV4KHTjGWYzWZ4vV68/fbb+MQnPoGTJ0/iq1/9\nKu7cuYMtW7aIKe1ytddCAerz8/Oora3F7t270d/fX3TZstVLnZXImCwieTXUZoSsmZPzbWxsDG1t\nbchms5iZmREJeWgpMQcRmdVqRVVV1Zovf7fZbHjxxRdRV1eHn/70p/jGN76B2dlZ7N69G7/2a78m\nHFY0y5LDE00mE3bu3AmbzYZQKJSjQQOL7chms6G6uhqJRMJwCq9KPk/WL7C03RhFeXAYzcx4Gbwu\nNBhwpx9/hyqfiMY9PPRknMlkRAjS0NAQOjo6sG/fPvT29sJisaCjo8MwrEhl7dAUk6whYKlTI5td\nTJy+bds2QQ6yU0O2SvI5NXjaQvqfCFm2NjaaoFfqjJGfK9+gcmhoCCMjI/B4PKiurkY8Hs/ZsFMm\nCIpiofcgx7fKYYd0njx15+WT1GGz2TA9PY3x8XGcPn0a1dXVOHbsGPbs2ZMjH1Ed+LWDwSAmJiZQ\nW1srZBaV85XyNNAqQlVECHfiUr1VCyvkGPpiCZGXq1ptyK1hedGI6lnL74mOeZjx0JOx2WwWlsvF\nixcxMjKCT37yk1hYWBBTzdbWVtHZeYPmXnRq9HJYELcWgMUGNzc3B4/Hg3379uH999/PIWsVafHv\nZLmEn8vDwSh8iL7Lt7BkPVHMVFf1HVm0NKglk0mMjIxgcHAQmUwGX/jCF9DW1obe3l4MDAwgFAqJ\n5DwyaJpOJNrd3Y3m5mbcvXsXFy5cEERBz4+uT+fSM+TZztLpNCoqKtDZ2YmRkRFMTU3BbrfjH/7h\nH7B3716YzWZ873vfQzgcXhKpQGX6fD7YbDa0tLSIOsqx01QXp9MpwtuMBjb5O5W0Vkhu4/dLZVL7\n4e2M+gKFqwFAPB7PWza/J42leOjJmI/gZrMZ8/PzGBoawic/+Un09fVhYWFBkAEnNOqs3Bogq4Vy\nsFIjpRVUkUgE77zzDtLpND7ykY/grbfeylm8wUleRqFQIHk6SF5sPnjc746gIl552kufORwOpNNp\nxGIxhEIhXLhwARUVFTh16hQ+9alPwe/3C50/mUzi9u3bqK6uNhywaOociURw9epVRCIRVFVVobOz\nExMTE2IAo+m1bNHxCAe73Y4Pf/jDqKurw/j4OC5fvozR0VHU1dVhYWEBP//5zzE7OyucWjzig+rm\n8/ng9XqxZcsWmM1msffYXfwAACAASURBVMGBUfpIm80Gl8slIi/KysrWfHCViViuB9d+qY3xkDWN\n1eGhJ2Pe0Gj0n5qaEkHqly9fRltbGzweT06IG+XZ5dZnJpNBOBwWjZaiJG7fvo2ZmRmEQiG43W40\nNjbi7bffxhNPPCE827KDY7lTSPpN9SCH1nJXbt0v8PvlsbZ37tzB2NgYHA4HPv3pT+PAgQMIhUI4\nf/48MpnFnBVVVVXw+/0IhUJwOp1LNroka66srAx2ux0/+MEPsGvXLuzfvx/bt29H5/8tlZ6YmEBf\nXx+Ae6vWuDwCANXV1aiurkYkEsHly5dx48YNDA4O4s6dO2hpaUEsFsPCwoIISQMWFzxw34PJZBKb\nG3g8HqW8wp8LcG+mQLHJ6/E++QxM5VyjH3KUUvvi+rfGyvHQkzFwT28jazcQCCAQCGD//v2Ym5vD\nf/3XfyEQCKCjowPHjx+Hw+FAJBIRjdbr9SISiQjLanp6GqOjoyL7VkdHB7Zu3YrW1lbU19fDZrPh\n5s2beOutt7Bv3z7hjFopVNobxSHLYXMbCSO92KjTEgEnEgn09/djbGwMNTU1ePrpp/Hxj38cd+/e\nxZUrVzAxMSHK8Pl8aGhoQH19PXw+H2pra5W6qM1mQ1NTEw4fPoxnn30WX/rSl3DmzBk8//zz+OAH\nP4hMJoOqqio8+uijKC8vR11dnViqTO2DfAt+vx+/+MUvMDc3h+npady+fRtdXV14/vnncf36dSQS\nCZSVlQkNmK+ey2YXY38jkQi2b98Ot9stsrYZPUOTaXHxh91uh9/vz8lfke95rgRcP+d1oM8onpvL\ne8Da7JLzsOOh2wNPBZXTxGq1ora2Fk899RTcbjcikQi+//3v44c//KEISaPGWV1dDZfLJeIr29ra\n0NbWhoGBAdTW1qK5uRmJRAI+n09YFJWVlXjnnXdw+/ZtHD16FHV1dQDuLQMmi6yQk0PW8/h98J+N\n3nqoGFDYF9UvkUhgYWEBPT09aG9vx9GjR/HRj34UsVgMPT09mJ2dzZE6SBZqaGhAMBjET37yE9TW\n1mL79u05TiwenmgymdDW1oZjx44hnU7jlVdewX/8x3+IJcH79+9HMpnE9PQ0nE5njqUdDoexsLAg\nlq6Hw2E4HA782Z/9GR577DHMzMzg6tWrS6IUZB03HA7D5/Ohq6tLbDyQTwsmQjabzZidnUU0GkVL\nS4vQ09faIuVlcqudVtPJujHBSP9/2KD3wFsFVBpmOp3GzMwMent7cezYMZSVleEzn/kMTpw4IYL1\nKZSspqYGbrdbdA4KdqdwpXA4LMibLPBEIoE9e/Ygm81iYGAAJpMJDQ0NIo2nkUyhslzkeyBQOSqy\n3gioOiofHGw2m5jmxuNxDA0NYWJiAnV1dfjMZz6D7du3Y2pqCmNjY5ibm1PeAyW4aW5uRkVFBQKB\ngHB48dV3vE5jY2Nwu93YsWMHPvaxj6Gurg5zc3MYHR2F0+lEOBwWu2vMzc0hEokIIqqsrEQ0GhWO\n3WPHjuHgwYNwuVwYGRnJyQshPweTyYR4PC7iouk7OcpB9RxpELfZbDnbMNE9rgch89A1GtS4Y1OG\nlipWB20ZK8C1MXL+UHIe2vaHSJMn7KGOASyumqqpqcHIyAguX74Mh8OBysrKHEdHbW0tstks3njj\nDXi9Xpw4cUIsUQXUoUeyrkx/yw4U7hTkSdfvJ7i2SCviyBru6+tDc3MzHnvsMbz00ksYHh7G+Pg4\n5ubmDCNICJlMBu3t7ZicnMTNmzdhs9nQ2toKAGK5uAwimra2Nmzfvh0ejwd2u13EfNMglk6nYbfb\nUVFRgfr6etTX1wu5AliUSX75y19iZGQEgUDAcIdxuvfJyUncvXsX3d3dwtmrqp8czQBADPKBQEDs\njiE/l5VCtuK5H0Veom3UJteiHg8CtGW8huChajx6gnbq4AH8ZPHKHTCTyWDv3r3YvXs3QqEQxsbG\nEAqFxBTXZDJhbm4ONpsNTzzxBAYHB9HT04OnnnpqiUPEqLPyDiMTVr7IjLWEyvo1AoWWpVIpxGIx\njI+P49atW2LW8dxzzyEYDOL06dMiKxt3KMnWNR804/E4tm/fDofDgZ/+9Keorq4WzjFVqBa9t5GR\nEYyMjMBsNqOtrQ179uxZkuksk8nA5/Ohv78fc3NziMViOTIVJyiy+vmAweseDofR0NCAiooKhMNh\nQ6uYP0seKsmlgkJhg/K1jaAiYgA5uU/kDHRyXdfLqfgwQZOxAryz0/8ARMfjiV+oY3BJgBrm+Pg4\nMpkMmpubhd5IUz0eU+pyudDZ2YkbN25genoa1dXVwjrmZCRbwPQdkRyvK59irsfsR9ZF+bNTHcfz\nfESjUQQCAVy5cgXbt2/Ho48+iqeffhq3bt0Sm7USofFl6So5iZNlQ0MD6urqUFVVhUAgILa358uR\nZSKn92c2mzE+Po7JyUnxLlU7gnCi4uSkIl6ZvMjJSxsZqCzMfIRG92K324VRoDqmmAEyX5vgz4kv\nm5bL5Peu9eLVQ5OxAiqCkZePqqwEcmxQwwwGgxgYGMCpU6fQ1dWFH//4x1hYWIDb7UY8Hhe5CLxe\nL1wuF5555hm89tpraGxsRHd3d07ZlFeASJbHPMuWGK+3StZYC6iux++f68IU4xsIBDAzM4P+/n44\nnU788R//MZ544gkEg0G88cYbCAaDQhqg+G0uF6hA74XkjoaGBpw6dQo/+MEPMDExIRx1wL20o/KO\nxvSc+EBKA4CKhIBcGYjrxPydcFILh8MYHBxER0cHGhsblRaxkYUpDyQmkwnBYBBlZWVCS6ZBqdiZ\niqqtUL25A5li5lUDIf9fW8WrhyZjAxhZYfmgIqhUKoX+/n5s27YNnZ2duHLlCuLxuNj7jkgrHA6j\nuroajY2N8Pv9YlECdVjVVNZoeqm6h/XqLNzSlHNicGdTMplEf38/pqam0NXVhcceewwnTpzA0NAQ\npqenEQgEckiRr1jMB/59IBCAx+NBV1cXmpubMTc3B7/fj4qKipxVcLJFWWiKrxrQ5LKIEGk5PO3u\nnM1mxXLpUCiEQ4cOwW63i3h0FSGr6sY/J6mCP+vVOs9oYKLnzx2DxVi72iJePTQZLwPFNHYVid+5\ncwfT09N49tlnEYlEMD4+jkQikZOEHABisRg+8IEPYGhoCLdv38aRI0eEVaiyflUddSPApQeCnCSG\nOnU0GsXU1BRu3LiB/fv34yMf+QieeuophEIh/OIXvxDb0PMsXyu5J5PJhFAohFu3buHIkSN46aWX\n0NPTg+9973s4fvw4tm7dKhbqcAtYdV/5IC/Q4LMkWpWWSqUwPj6OK1euYGZmBuXl5ejo6MDzzz8v\nZkXcii50X/w69JxtNhvi8bhwIMurLIslUQLJJpTfWJXuUlu/6wsdTbHGkMk4k8kgkUiIZN6nTp3C\n3bt38e6774q9xjghV1RUwGazoaenB/Pz8+js7ERTU5PSOi+lzkHkRpo67Vt3+/ZtNDU14Xd/93ex\nb98+eL1enDt3LmfHYyB3m6WVLq0lArLZbNiyZQuCwSDGx8fF8uRTp06hqakJbrc7h1TzEVe+Z8xl\nlExmcRuj0dFR3LlzB5OTkzh27Bja29tF7ol4PI5YLCbaRLG7x/CBg2SJhYUFmM1mkamOBrNiy6H/\n+X3Sgg7V8uZS4InNAh1NUSKQGztpj7S9TTgcRmtrKyoqKhAMBnOWLVssFkSjUaTTaWzZskWEd9XX\n1+dER3AHlHzNjYQ8jSfrPRgMYnp6Grdu3cLhw4fxxBNP4ODBg7h69SqmpqYQi8WWLFigmOPV5Dig\nZ0I7Wng8HiwsLOD48eO4efMment7UVdXh507d4rQN3nw5LMPlTNMdTzFjY+MjKCnpwepVArPPPMM\nuru7xX3FYjExAFGbWMl74xYyl0iKkSlkOYu3IXIAG+VLXk79CqGUjIhSgibjdYTZvLgLh9PpFFnU\nLl++jPr6ejz++OMihKuioiJnV+BsNouGhgYcPXoUIyMjmJycRFNTU05kAHD/GrU8VTeZTCIF5Ojo\nKK5evYrGxkb8zd/8DXbv3o3p6Wn86Ec/ykmGw+UC7qBaLUjWCYfDqK+vR21tLcrLy7Fv3z4MDw9j\ndHQUZ8+eRTQaRVtbGw4fPoyKigoRkcLTP/J7VD2DdDqN27dvo7e3V5T34Q9/GA0NDaiqqkIoFEIw\nGBQr7OT8v8XeMydRkoDsdju8Xi9MJhNcLpcymsOo3vJycbK2uSyx0jamiXbl0GRcAKuRBWjaTtv9\nUEjT9PQ0XC4XnnvuOVy9ehXj4+Mi9wB1imAwiI6ODtTU1OCtt94S+6upnD4bDa650vT85s2bmJqa\ngsfjwT/+4z+ipaUFU1NTeO2113K2Q6JzgPWRXMhCnJ+fh8/ng8fjgdfrhd/vR11dHdra2nDy5EmM\njY1heHgYP/7xj8XechRp4XQ6xSag8uo9evahUAiZTAadnZ345Cc/idraWhEdk8lkMDc3BwA50Q5G\nEQyFwC1yOoeSVvE482KsUh4VRI5GciKTrFZIujHCekgZDxO5azI2gKphrXQKxvcAoy2SZmdn0djY\niNbWVkxMTCCRSAgHEx1LCWdaW1sxOjqKbDYrVu0VuuZ6gU9xKSxvamoKw8PDqK+vx8svvywiGW7c\nuCFIgu5Jtg7Xum5capCJNBKJIBaLwe12o62tDdXV1SgrKxNpUoHFWGA6jhb6EIiILRYLOjs7UVVV\nhb1796K5uVk4LkOhkLD+CcVarfnuS4acNU0ln6jAJS4ezsbLKDZ6yAiFHKNG0T+FynnQocnYACpH\nh2ydFOpcqsZGW+dkMhkMDg5i27ZtOHDgAAYGBkRaRbJeIpEIbDYb9uzZg/Pnz+PatWs4cuSI2Pl3\nPZ15qrL5FDaZTAoNuK2tDV/72tfQ0tKCyclJ/OxnPxOZ4ngu32KcTKsB19XpujSF57uBeL1eoeMf\nOHAgh8B5IhyyHAncoqfy0+k0fD6f+J+H53EU+37yRXnwEELKr007ndP3hbKn8dWjwD1ZTG5PRlhu\nRFGxkAl6rdpzqTq8VXjoyVhuOCrCzZfxTA43U01F5ThcAGLVWG9vL06cOIGWlha8/vrrCIVCOfkp\n4vE4nE4njh49ivHxcVy4cAFbtmxBV1dXweQycn2MBg+5sxNoyprJZERWs3g8josXL8Lv9+PQoUP4\n0pe+BI/Hg6tXr+LmzZtiGTOVJ29Tz3+vNTgJkgWeSqXQ3NwsVtbxiI1oNIpYLCbO5c9BZUHScTyC\nQiY3uT0sF6pz5bJphuVyuYR2zRd+5Lu+LEnI6ThV9ZAdfnzhkRzemK/ucnlG9VvpDCLfILYZ8NCT\nsZGOR42CYnzzWSycAGTnCD9OzmFAGbDm5+fR3t6O9vZ2DA0NIZVK5cTEplIpVFZWoq2tDTdu3MDd\nu3fR1dW1rJAs3qFU9yyTEZ8CU0dPJBIYHh4WuZ1/8zd/E3a7XSSA58TGr1vstHQtIF+DtmOicDtK\n5k+RH9wqVpVh1D7oGJmI1xPyQEkzjUQiAZfLVdT5sgUsL/eWr6MCEbAc+bLcSBgj8lZp5KpjCtV5\ntQPjRuOhJ2MZqs4mW1v8WCLsbDYrNEZVB5dXNZlMJiQSCdhsNvT19WFkZATHjh1DIBDAwsKCSDhO\nllAgEIDD4cCJEydw+/Zt3LhxA3v37jXcBt7ovujeZAuEflOHotSUDocD4XAYFy5cwPz8PA4cOIBv\nfvObcLvduHnzJk6fPi0kiXwJ0jcKspUfCoXQ0dEBu92Ovr4+8Z7yEagRSauOux+gNkEySjweXxJR\nYTToFkpKlO+aBC7JqCAPxipNW24TqrhmeaZC/UHug/LnRoPpRrbDlUCTsQJGloNq5Ocrn8iKVaWz\nJEuGND1qQOTBj0ajSCQS2L17N/r6+sQWQtTpKPl6dXU1Ojs70dvbi0gkgvLycnGd5ZCDUcOkaTew\n6LGfmZnBxMQEgsEgOjs78ZnPfAZWq1VsDkopJnmO3VIA78jhcFhsVkqzjnyzCjqvlEEzFqfTCZ/P\nt+T7QkS5UueZahaV79x85fA6cR2e5/rg9eXJo2T5D8CSz+V7LnVoMpYgj6oqTZl/LmtmlGOWNyg6\nPpVKCWmCrGKykE0mE86dO4fjx4/jySefFE4wkivIGqIscLt378bly5fR3NyMjo4OwyW+RvenmubR\nIJFOpxGPx3H+/HkkEgk88sgj+PKXv4yqqipcvHgRPT09Ocl3yAlUSgRG95lOpzE1NQWTyYSmpiZM\nTU2JYwoRcqmC15naB31ejE5aDGEZSQ4qEs13jKreMskC95bTE+Tl3XQtMmy4H4ecrDxlwEZKY2sF\nTcZY2jj46K/yPBs5a4hwAbV+TNnC6FqcnIHFxtTT04MtW7bgySefxJtvvolYLIaKigpRFlnQO3bs\nQDgcxuzsLDweDyoqKnJCx3gUANWNfvOGLoec0Q7WPp8PH/rQh/Dyyy/D6XSit7cXc3NziEaj4v4o\nnIuslVJq+FxqoHwgzc3NiEQiCAaDYhnxZgS1ObPZLJLMx2IxkdmvECGrvi92IF1O2fIArZIMeB/h\n56pylJhMppzUstR+iaDlPsdRSoaCEe7/9g8lgHwOG1myIAIutJyVa2XcguANjnJTOBwOQZ6JREJs\nuNnY2AizOXfjRyojlUqhq6sL9fX1GB4eFrkvirEIZMuIFhDEYjH09vYiFoth3759+I3f+A3EYjFc\nvXoVY2NjIhm6fB+Frnc/wOtDlj7tviLnpdiM4IMh3R/XuYu5L5WeW+hY1blGujD9pgGfJx/KVwf+\nt7wqUHaCU9IkvnqSl0dGRqm1TxW0ZQzjCAP6jiAv31Wdu1wLg84nizmVSsHv92NgYADHjx/H2NgY\nLl26lJNyM5NZ3NSyoqIC+/fvx/nz5zEyMoKmpiZUVFQAgGE4Ht0Db7TBYBBvv/02vF4vXnjhBXz2\ns5+Fw+HAxYsXMTQ0JEKnqMFvhsbNZze0U/Pc3BxqamowOjoq4og3Kxnz5FJ8J2oe5gYsvz2uB1R1\nKFazLnQu9R+e44WWn/MNFzbDe9Zk/H+Q5Qf6DECOPkovnFtX+SzrYq9J16CtbhYWFnD16lVs3boV\nO3fuxKVLl+B2uwXZAouShcPhwKOPPorTp09jbGwMhw8fFknHOTjxcGtqYGAAly5dwqc+9Sk88cQT\naG9vxzvvvINAIIB4PC52Jclms6KRL/c+7xeoE8ZiMZhM/7+9c2tqq4ri+D8kOblRIpdCgNIBdVpK\n69h2mBZv1anjOL74oG9OX/RRv4HfwM/hN7BPti+2tkPbsaOjw6gFaaUSSoBAyElykhDwgVm7K5uT\nkEBCzgnrN8OUktvJOXv/z9prrb2WB4lEAqVSCd3d3VhfX4dhGGV+fbfA/afAbqeYeDwOAKrPYiu+\nTyMFvdabiT5XSZT1lWQt79VqRIyBPf7Oar/r/uKDWol2A0NfaqVSKSQSCYyNjWF+fh6FQqEsP5bK\nHUajUbX7za4hph4BJ8t4enoaCwsL+Pjjj/HFF1+gq6sLP//8M5LJpDoGEmIKsFBGQqXv0GrsfJH0\nHciv2NXVhVQqtee1brD4dfRdgbwrylH78atZsQdZQdYakOTPpfgFXx245ZqKGFfAzgKktC/DMFAo\nFA5lVfHBSb/z1B1g14f79OlT+Hw+TExM4NmzZ9jY2EAwGFRZDGTlTk5OYmlpCQ8ePEAsFsPZs2fL\nclEp5c40Tdy5cwcbGxv4/PPP8e233+LcuXO4desWXrx4URYc8vv9yhrmKwG9p5yTqObD3tnZQSKR\nwOjoqNrME4lElHi1yqKsF7oGdH0p7kDpj3pfxlYfa61xhWqrTLsYhe4ypNUg953bva9TETFG5Ylr\nB++6oV/8aq+r53P1AMbm5ibOnz8PAHj8+LEqIMQ3hXi9XsRiMYTDYaytrWF7exuBQABer1elyKXT\naUxPTyMUCuHatWv48ssvEY1Gce/ePaysrKgbAu8uQlSbGE6GrHv6ndwW1CGj0u5Kp8PjB5Zlwefz\nIZvNqr/RaqYVIqSPlUrHoJ93u3FVaY7wmAfPjSfjQ8/5d4MgixjXiL7EoourW1WNnNQk+vF4HD6f\nD6dOncL4+Dj+/fdf5PN5hEIhZR2Rxfzhhx/iyZMnePDgAaampuDz+bC5uYkff/wRxWIRN27cwI0b\nN2BZFu7du4dkMqmaTnKrt50g6546c1Mzz1QqhUAgUHOOtpMgEQKgtngbhlFmEbfKMt6vHvR+N3Pd\n6tXnGwXnSHj5So1+SIh5ipzTr6+IcY1UmqzNDGjxmrXxeFw1tBweHsbdu3dVDzQSZCoPeeHCBViW\nhbt376JUKiGdTuObb77BlStX4PF4cPPmTRWco9dS/jB9ZrvArUNeiY0CXblczlXpT4Te6SMUCiGX\ny2FrawuhUKiqRdpM9M+0O4b9fMt66hr3A1MuMRfefD5f9lp9I5ZbbrSSZ1wHlQYM/dvIC87v7jyg\nF4/HYRgGuru7Vf0I3gg0m82iWCwiFothcXERS0tL+PTTT3H9+nWEw2H8/vvv2NjYQD6fL6sxQJsH\n3DBo64FPUNqyTV2bKTPGaRtWaoEv06kjNd1U+UqnlfAgt57/bOeK0P3FlL1ENcC5W65QKKgf/caj\nz8lWN2OoFbGM60TfB8/vxI0UZBpEPK/X4/FgYWEB2WwWH3zwAW7dugXTNFXb9kAggHw+r+pafPXV\nV4hEIjhz5gxu376tWgDR+9O/rfQvHgU0Gf1+v7KGY7EYenp6kEqlVHNQN31/Pta2trZUdxIaLxTI\na8VxVfs/nWMyMvhzaMyT8PLn29V8ocftDCP99W5AxLhOdMGlwAEt9xuda6lbEJlMRonq1NQU5ufn\n8ddffyEYDCprNxKJIBaLwTAMJBIJfPfdd7h06RK6u7sBvOwTV2+qkVvhbgpiZWUFnZ2dyt9ab/lH\nJ0HX0+fzYW1tDf39/fD7/WXV6VoFT73ThZOnS/LaFGTtc/RV6X6uDqLV378e3GG/Owg9tQZAmR+r\nWeh+tGQyCcMwcOrUKfj9fqTTaZRKJfT29mJgYAA7O7udQqgO8vLyMjKZjG02iJsGbCPg/mHytVdr\nIOAGSHipfooT0MWRBJd8v9T3kVZ23J3EW5Xp26j3y7bQXSJuQSzjGqmW/kYXnleNatZnEtlsFtPT\n0wgEAujr61MdQcLhMCzLwubmpirbOTk5idu3b2N5eRnvvvuuKq6uW8fHBfIbB4NBRKNRJBIJ2yLr\nboJS9QzDUELW6BgGUP3GzcdrJSEmI4BccHw3K/eD2wVU7SziasLstrEtYlwjlQYBr9sAlHfz0AdP\nvYPDTozJV005xD09PZicnMSvv/6KZ8+eIZlMKkuDNob4/X5cu3YNT58+xS+//ILLly+XZWrwf/Vq\nb+0KrRx6e3uxurqqruN+aVlOgo8zurFGo1H4fL4D50/vZ1XrLgA9BY2neJLo8qJa9Fxu+XLsSmfq\nj1XjIPn+TkHcFHXAXRO6FaBbIuQHa+SSib8XTT7aeXXy5EmcPHkSxWJRNaukY7AsC+FwGCMjI8hk\nMioFitfc8Pv9bZljbAdfDmcymTI3kxuXuLooUn3serII9FWenvlQKSuCv57OHwkwZUHQ8dGYK5VK\nZQE5PUe4HvTXtSqlrxEcDzOoQdgNQL6c0pdWh53Qdq/X6x/Pzc3h77//xsWLF3HhwgWYponV1dWy\nrA+yAsPhMN5//3389NNPGB4expkzZ5Sw7+yU71SrhFtyNqvBG5K6MZOC4NeBjAEqtxoOh2sW40or\nOf0z+GfRDY1uZLRS4wHt7e3tsu7T+qqjUhCu0rVw4zWqBxHjQ2LniqiU90jP1/9WD/oyjPJl5+bm\nkMvlMDg4iK2tLayvr6Ozs1M9n6yl7u5uVeXrtddeKwvk1eJndLsQE7rlaOejdBsej0f5jg+SW1vt\n2vJxx4WUW8HcxaCnfB70mI4TcnYaABdf2p5Jk10fgIddAvPBT+9DBYDm5+cxODiIqakpBINBmKap\n0t2A3aBfqVTC9evXMTExgUePHmF5eVn579wuRrXCr1W73FyAlzdmKhRU6/Xcb0ySj5d3pvF6vYhE\nIgiHw2oXaD6fh2VZsCxLFdKyKygv2CNi3EB45Jgsg0bnr1IEmgdoqMIasFtIaHFxEe+88w68Xi8s\nyyoL+mWzWfh8PoyPj6O/vx+zs7MwTdM2ou1m/1s1uOXWLmLBN+8cJpNCPy98y7VhGHsEmHbB0e5G\nu4wKfeXYTjfARiJifEj44NIjv80QtEoDmSZOoVDA2toaotEoBgcHVfWqnZ2XxeHz+TxKpRJGR0fx\nyiuv4Pnz5yoDg+dLt/PEoe9F7YrcvOkD2Jt9UOuY42PUriUSgLJVHgXiePlW/dzZBdX0x4S9iBgf\nALvorT7w9B55jRZku80nwG5Qb2NjA/fv38e5c+dw8eJFtSGEAnT5fB65XA79/f146623kMvlEI/H\nlWhXeu92gVKwKCMlHA6r4jpupVL2w36QyNo93zAMhEIhFZyjYC+vmULwsULvJT7i+pCzdQAqpfXQ\nAKWUMR7UOAr4cZimiYWFBfT392N8fByZTAamaZalxlH926tXr2JmZga//fab6y3EWqHIv8ez2z3a\nsqxWH1JL0NPMfD6f2jxEW6p5UR5yj+k3LjsxFupDxPiAVEsur2WjR6OtTrvsjWQyiefPn+P06dPw\n+/2wLKtMbMmtceLECYyMjKgiQ9z33c7WDQWbgPZOm6olVYyyasiAILdWpdoSOroAt+uqqpm070w7\nIrg/jTf95IJGA5UP6EbuFOLvy+u+ZrNZ/PfffzBNE++99x5GRkZgmqYSWMoDpTrJ58+fx+PHj1Vl\nN4qe6wG9dphktOMuGAyqDS/cz+9GKlmrPG1Pv44UmAuFQiotjjYO6XWBa705u/X8tRoR4wZgJ1Y8\nGEIDuNLOpsNSySKhSbi0tIRgMIjh4eGyJSmvDxsIBDA0NISenh6srq6qLAz+GW7cnWYHiRD1jrPb\ngdcO6GON/83jK0gd0gAABUtJREFU8ZTVCeZZOtWyS0Rom4eIcYOxC+bRRNivMthhLM9KQb3t7W2s\nra3hn3/+QSwWw+XLl7GxsaH8f/Ra6gj95ptvYnZ2FjMzM6pwPRdlN1uOBGWYpNNptTXcSdXODspB\nbiJ8p5yeIdGOKyInI2LcYHRXBQke71G2n9/tsJYZfS5tV/V6vXjx4gXu37+PoaEhvP766ygUCshk\nMntaL0UiEVy9ehWBQACzs7NlOc3tAn1nyqQgV1O7WMTV4MJKnWLofHA313E4F05DxLjBVPPbHVWZ\nRhIX7i7Z2dktIJNMJnH27FkMDQ2pXVLAy6ptW1tb6O7uxsjICFZWVlRaHH2XdljGe71eZLNZrK2t\n2aZptTu6W0u3gvXnCEeDiHGToSV+sVhUQSPg5fKwmbu/yMXAI+UzMzNIpVKYnJxEb28vTNNUm0Go\n0IzP58Po6CgmJiYwNzeHlZUV9V3axULu6urC4OCgKhJ0XMSHxiPt2qRKfTQ+db+xuCiODhHjBmOX\nYsb/RtHrRgfxKh2LnsHR0dGBP//8E3Nzc/joo49w6dIllc5G9XzT6TTS6TTGx8fR2dmJJ0+eIJVK\nwbIslWHhdksyl8shnU7DMIwjzwdvJTxVjVw1Pp9PjUke72inoK0bOB4j8Aixy2ywsy4qTf5mWSBU\nv9fj2W1Wubi4iFwuh6GhIQQCAViWVdbynER3bGwMAwMDWFpawtbWFgKBgOvFi25KgUBA+dePi+Wn\np1jS6oy70ewygoTm494Z5SL44Carkrceb4avTp9EFJjZ3t5WbZcePnyIVCqFqakptVQlC5n8qgMD\nA7hy5QpSqRQePXqkSnG6dZLSdaDdh9Tq/ThhV7iHgnfkthEXxdHjSjHmd3TevqVavq/uo9Ufr+WH\nP7fSZ/Jj5O4BPcOCcntJIO0Cf4fBbss2WT+0NC0UCvjjjz/g9/vxxhtvIBQKIZfLKcu4WCwilUqh\nWCzi7bffxquvvoqHDx/Csqw9FlYjj72Z0FZwOudu730HlAsq8HJ+VHs+38TBN7wAKMs9tps3QnNw\npRg3mkaLiV1k2s7ireY3brSPjiarfgPp6OhAPB7HyMgIxsbGytK+eHCnr68Pp0+fRi6XUzv0qn2W\nk6GUtkAgoEqPHifsjAz9Mf3/Tr+m7YArO31w/1YlC40LHR9MdkKrL7srLcP5Z1VzMeiWsH5MRKlU\ngt/vRyQSKUuvauRWaTv4Oeno6IBpmirD4rPPPlOdpcmdAuz6nE+cOIGvv/4aP/zwg3oOsV/g0gnQ\ncRmGgU8++QSxWAypVEo97lY/OF0HwzDg9Xpx8+ZNrK+v1+0L5+OCfqdVhF29YqGxuHP0tQG69dGq\nY6DJF4/HkUgkVLoTPU41Cvx+P4rFIsLhMPr6+lQdAzdit7HBrULcDEiMq5XXFBqPKy1jAFV9YkB9\nxbZrdVPYLd+qPb7f8dE2VCeUb9zc3MTy8jLu3LnT6kNpOplMBt9//32rD0MQyhBzQBAEwQGIGAuC\nIDgAEWNBEAQHIGIsCILgAESMBUEQHICIsSAIggMQMRYEQXAAIsaCIAgOQMRYEATBAYgYC4IgOAAR\nY0EQBAcgYiwIguAAPFISTxAEofWIZSwIguAARIwFQRAcgIixIAiCAxAxFgRBcAAixoIgCA5AxFgQ\nBMEBiBgLgiA4ABFjQRAEByBiLAiC4ABEjAVBEByAiLEgCIIDEDEWBEFwACLGgiAIDkDEWBAEwQGI\nGAuCIDgAEWNBEAQHIGIsCILgAESMBUEQHICIsSAIggMQMRYEQXAAIsaCIAgOQMRYEATBAYgYC4Ig\nOID/Ae82EHOp24jaAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "gc0fReyWSrXH"
      },
      "source": [
        "## Are we going to learn to do Linear Algebra by hand?\n",
        "\n",
        "Let me quote your seventh grade math teacher:\n",
        "\n",
        "\n",
        "> \"ArE yOu GoInG To CaRrY a CaLcUlAtOr ArOuNd wItH yOu EvErYwHeRe YoU gO???\"\n",
        "\n",
        "\n",
        "Of course you're going to carry a calculator around everywhere, so mostly **NO**, we're not going to do a lot of hand calculating. We're going to try and refrain from calculating things by hand unless it is absolutely necessary in order to understand and implement the concepts.\n",
        "\n",
        "We're not trying to re-invent the wheel.\n",
        "\n",
        "We're learning how to  **use** the wheel. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "YceHUblDSHOF"
      },
      "source": [
        "# Linear Algebra Overview/Review:"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "ke1ffJRNMOnv"
      },
      "source": [
        "## Scalars: "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "ODzKTJLGTnBz"
      },
      "source": [
        "A single number. Variables representing scalars are typically written in lower case.\n",
        "\n",
        "Scalars can be whole numbers or decimals.\n",
        "\n",
        "\\begin{align}\n",
        "a = 2\n",
        "\\qquad\n",
        "b = 4.815162342\n",
        "\\end{align}\n",
        "\n",
        "They can be positive, negative, 0 or any other real number.\n",
        "\n",
        "\\begin{align}\n",
        "c = -6.022\\mathrm{e}{+23}\n",
        "\\qquad\n",
        "d = \\pi\n",
        "\\end{align}"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "SIyzbJFxamu1",
        "outputId": "bc411f5f-de0e-4c05-e179-d8c5b59d47e2",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 363
        }
      },
      "source": [
        "import math\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "\n",
        "# Start with a simple vector\n",
        "blue = [.5, .5]\n",
        "\n",
        "# Then multiply it by a scalar\n",
        "\n",
        "green = np.multiply(2, blue)\n",
        "\n",
        "red = np.multiply(math.pi, blue)\n",
        "\n",
        "orange = np.multiply(-0.5, blue)\n",
        "\n",
        "# Plot the Scaled Vectors\n",
        "plt.arrow(0,0, red[0], red[1],head_width=.05, head_length=0.05, color ='red')\n",
        "plt.arrow(0,0, green[0], green[1],head_width=.05, head_length=0.05, color ='green')\n",
        "plt.arrow(0,0, blue[0], blue[1],head_width=.05, head_length=0.05, color ='blue')\n",
        "plt.arrow(0,0, orange[0], orange[1],head_width=.05, head_length=0.05, color ='orange')\n",
        "plt.xlim(-1,2)          \n",
        "plt.ylim(-1,2)\n",
        "plt.title(\"Scaled Vectors\")\n",
        "plt.show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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VKKKR2SUB8HBM3MBlPPX4Un2+52atW3aDwpvdbnY5ACCJiRu4xPEfjqt15y9l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\nsBCCGwAAC/n//qLKhfEwZywAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f038c9fe588>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "d3tU-l96SNa3"
      },
      "source": [
        "## Vectors:"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "TRhtzFMwTz0Z"
      },
      "source": [
        "### Definition\n",
        "A vector of dimension *n* is an **ordered** collection of *n* elements, which are called **components** (Note, the components of a vector are **not** referred to as \"scalars\"). Vector notation variables are commonly written as a bold-faced lowercase letters or italicized non-bold-faced lowercase characters with an arrow (→) above the letters:\n",
        "\n",
        "Written: $\\vec{v}$ \n",
        "\n",
        "Examples:\n",
        "\n",
        "\\begin{align}\n",
        "   \\vec{a} = \n",
        "   \\begin{bmatrix}\n",
        "           1\\\\\n",
        "           2\n",
        "    \\end{bmatrix}\n",
        "    \\qquad\n",
        "    \\vec{b} =\n",
        "    \\begin{bmatrix}\n",
        "          -1\\\\\n",
        "           0\\\\\n",
        "           2\n",
        "    \\end{bmatrix}\n",
        "    \\qquad\n",
        "    \\vec{c} =\n",
        "    \\begin{bmatrix}\n",
        "           4.5\n",
        "    \\end{bmatrix}\n",
        "    \\qquad\n",
        "    \\vec{d} =\n",
        "    \\begin{bmatrix}\n",
        "           Pl\\\\\n",
        "           a\\\\\n",
        "           b\\\\\n",
        "           \\frac{2}{3}\n",
        "    \\end{bmatrix}\n",
        "\\end{align}\n",
        "\n",
        "The above vectors have dimensions 2, 3, 1, and 4 respectively.\n",
        "\n",
        "Why do the vectors below only have two components?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "GzxZcC8fdf5s",
        "outputId": "4c294194-a9eb-4284-8e88-cf30d5cd681d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 363
        }
      },
      "source": [
        "# Vector Examples \n",
        "yellow = [.5, .5]\n",
        "red = [.2, .1]\n",
        "blue = [.1, .3]\n",
        "\n",
        "plt.arrow(0, 0, .5, .5, head_width=.02, head_length=0.01, color = 'y')\n",
        "plt.arrow(0, 0, .2, .1, head_width=.02, head_length=0.01, color = 'r')\n",
        "plt.arrow(0, 0, .1, .3,  head_width=.02, head_length=0.01, color = 'b')\n",
        "plt.title('Vector Examples')\n",
        "plt.show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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mTpQkeTyvKijoZIsnAgB0h3Yb9IgRI5ScnKxp06bJ4XAoIyNDWVlZCg8P15gx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\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f55ce7ce438>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "Q2pNvak3gDGY"
      },
      "source": [
        "In domains such as physics it is emphasized that vectors have two properties: direction and magnitude. It's rare that we talk about them in that sense in Data Science unless we're specifically in a physics context. We just note that the length of the vector is equal to the number of dimensions of the vector. \n",
        "\n",
        "What happens if we add a third component to each of our vectors?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "BezrgDoH-Ky-",
        "colab": {}
      },
      "source": [
        "from mpl_toolkits.mplot3d import Axes3D\n",
        "import numpy as np\n",
        "\n",
        "yellow = [.5, .5, .5]\n",
        "red = [.2, .1, .0]\n",
        "blue = [.1, .3, .3 ]\n",
        "\n",
        "vectors = np.array([[0, 0, 0, .5, .5, .5], \n",
        "                    [0, 0, 0, .2, .1, .0],\n",
        "                    [0, 0, 0, .1, .3, .3]])\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": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "Pzg99dFw-Oj8"
      },
      "source": [
        "### Norm of a Vector (Magnitude or length)\n",
        "\n",
        "The *Norm* or *Magnitude* of a vector is nothing more than the **length** of the vector. Since a vector is just a line (essentially) if you treat it as the hypotenuse of a triangle you could use the pythagorean theorem to find the equation for the norm of a vector. We're essentially just generalizing the equation for the hypotenuse of a triangle that results from the pythagorean theorem to n dimensional space.\n",
        "\n",
        "We denote the norm of a vector by wrapping it in double pipes (like double absolute value signs)\n",
        "\n",
        "\\begin{align}\n",
        "||v|| = \n",
        "\\sqrt{v_{1}^2 + v_{2}^2 + \\ldots + v_{n}^2}\n",
        "\\\\\n",
        "\\vec{a} = \n",
        "\\begin{bmatrix}\n",
        "3 & 7 & 2 & 4\n",
        "\\end{bmatrix}\n",
        "\\\\\n",
        "||a|| = \\sqrt{3^2 + 7^2 + 2^2 + 4^2} \\\\\n",
        "||a|| = \\sqrt{9 + 49 + 4 + 16} \\\\\n",
        "||a|| = \\sqrt{78}\n",
        "\\end{align}\n",
        "\n",
        "The Norm is the square root of the sum of the squared elements of a vector.\n",
        "\n",
        "Properties of the Norm:\n",
        "\n",
        "The norm is always positive or zero $||x|| \\geq 0$ \n",
        "\n",
        "The norm is only equal to zero if all of the elements of the vector are zero.\n",
        "\n",
        "The Triangle Inequality: $|| x + y ||\\leq ||x|| + ||y||$\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "UOr0BCxn-Wlh"
      },
      "source": [
        "### Dot Product\n",
        "\n",
        "The dot product of two vectors $\\vec{a}$ and $\\vec{b}$ is a scalar quantity that is equal to the sum of pair-wise products of the components of vectors a and b. An example will make this make much more sense:\n",
        "\n",
        "\\begin{align} \\vec{a} \\cdot \\vec{b} = (a_{1} \\times b_{1}) + (a_{2} \\times b_{2}) + \\ldots + ( a_{n} \\times b_{n}) \\end{align}\n",
        "\n",
        "Example:\n",
        "\n",
        "\\begin{align}\n",
        "\\vec{a} = \n",
        "\\begin{bmatrix}\n",
        "3 & 7 & 2 & 4\n",
        "\\end{bmatrix}\n",
        "\\qquad\n",
        "\\vec{b} = \n",
        "\\begin{bmatrix}\n",
        "4 & 1 & 12 & 6\n",
        "\\end{bmatrix}\n",
        "\\end{align}\n",
        "\n",
        "The dot product of two vectors would be:\n",
        "\\begin{align}\n",
        "a \\cdot b = (3)(4) + (7)(1) + (2)(12) + (4)(6) \\\\ \n",
        "= 12 + 7 + 24 + 24  \\\\\n",
        "= 67\n",
        "\\end{align}\n",
        "\n",
        "The dot product is commutative: $ a \\cdot b = b \\cdot a$\n",
        "\n",
        "The dot product is distributive: $a \\cdot (b + c) = a \\cdot b + a \\cdot c$\n",
        "\n",
        "Two vectors must have the same number of components in order for the dot product to exist. If they lengths differ the dot product is undefined."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "IUeBZtVr-nro"
      },
      "source": [
        "### Cross Product\n",
        "\n",
        "The Cross Product is the vector equivalent of multiplication. The result is a third vector that is perpendicular to the first two vectors.\n",
        "\n",
        "It is written with a regular looking multiplication sign like $a \\times b$ but it is read as \"a cross b\"\n",
        "\n",
        "The cross product equation is a little complicated, and gaining an intuition for it is going to take a little bit more time than we have here. I think it's the least useful of the vector operations, but I'll give you a short example anyway.\n",
        "\n",
        "\n",
        "Assume that we have vectors $x$ and $y$.\n",
        "\n",
        "\\begin{align}\n",
        "x = \\begin{bmatrix} x_1 & x_2 & x_3 \\end{bmatrix}\n",
        "\\qquad\n",
        "y = \\begin{bmatrix} y_1 & y_2 & y_3 \\end{bmatrix}\n",
        "\\end{align}\n",
        "\n",
        "The cross product can be found by taking these two vectors and adding a third unit vector to create a 3x3 matrix and then finding the determinant of the 3x3 matrix like follows:\n",
        "\n",
        "\\begin{align}\n",
        "x = \\begin{vmatrix} \n",
        "  i & j & k \\\\\n",
        "  x_1 & x_2 & x_3 \\\\\n",
        "  y_1 & y_2 & y_3 \n",
        "  \\end{vmatrix}\n",
        "\\end{align}\n",
        "\\begin{align} =\n",
        "i\\begin{vmatrix}\n",
        "x_2 & x_3 \\\\\n",
        "y_2 & y_3 \n",
        "\\end{vmatrix} \n",
        "+ j\\begin{vmatrix}\n",
        "x_1 & x_3 \\\\\n",
        "y_1 & y_3\n",
        "\\end{vmatrix} \n",
        "+ k\\begin{vmatrix}\n",
        "x_1 & x_2 \\\\\n",
        "y_1 & y_2\n",
        "\\end{vmatrix}\n",
        "\\end{align}\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "drCVY_F8SaPI"
      },
      "source": [
        "## Matrices:"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "dKYeFAUbaP4j"
      },
      "source": [
        "A **matrix** is a rectangular grid of numbers arranged in rows and columns. Variables that represent matrices are typically written as capital letters (boldfaced as well if you want to be super formal).\n",
        "\n",
        "\\begin{align}\n",
        "A = \n",
        "    \\begin{bmatrix}\n",
        "           1 & 2 & 3\\\\\n",
        "           4 & 5 & 6\\\\\n",
        "           7 & 8 & 9\n",
        "    \\end{bmatrix}\n",
        "    \\qquad\n",
        "    B = \\begin{bmatrix}\n",
        "           1 & 2 & 3\\\\\n",
        "           4 & 5 & 6\n",
        "    \\end{bmatrix}\n",
        " \\end{align}\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "4oKAHHil-0bm"
      },
      "source": [
        "### Dimensionality\n",
        "\n",
        "The number of rows and columns that a matrix has is called its **dimension**.\n",
        "\n",
        "When listing the dimension of a matrix we always list rows first and then columns. \n",
        "\n",
        "The dimension of matrix A is 3x3. (Note: This is read \"Three by Three\", the 'x' isn't a multiplication sign.)\n",
        "\n",
        "What is the Dimension of Matrix B?"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "VqWzluoD-9Pf"
      },
      "source": [
        "### Matrix Equality\n",
        "\n",
        "In order for two Matrices to be equal the following conditions must be true:\n",
        "\n",
        "1) They must have the same dimensions.\n",
        "\n",
        "2) Corresponding elements must be equal.\n",
        "\n",
        "\\begin{align}\n",
        "    \\begin{bmatrix}\n",
        "           1 & 4\\\\\n",
        "           2 & 5\\\\\n",
        "           3 & 6 \n",
        "    \\end{bmatrix} \n",
        "    \\neq\n",
        "    \\begin{bmatrix}\n",
        "           1 & 2 & 3\\\\\n",
        "           4 & 5 & 6\n",
        "    \\end{bmatrix}\n",
        "\\end{align}"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "MYwxF4R8_Gnf"
      },
      "source": [
        "### Matrix Multiplication\n",
        "\n",
        "You can multipy any two matrices where the number of  columns of the first matrix is equal to the number of rows of the second matrix.\n",
        "\n",
        "The unused dimensions of the factor matrices tell you what the dimensions of the product matrix will be.\n",
        "\n",
        "![Matrix Multiplication Dimensions](https://encrypted-tbn0.gstatic.com/images?q=tbn:ANd9GcRunZv20HXxTMUgrkfdER06lPnMj0HpwDU_2i4IEHsBM5098440Jw)\n",
        "\n",
        "There is no commutative property of matrix multiplication (you can't switch the order of the matrices and always get the same result). \n",
        "\n",
        "Matrix multiplication is best understood in terms of the dot product. Remember:\n",
        "\n",
        "\\begin{align} \\vec{a} \\cdot \\vec{b} = (a_{1} \\times b_{1}) + (a_{2} \\times b_{2}) + \\ldots + ( a_{n} \\times b_{n}) \\end{align}\n",
        "\n",
        "To multiply to matrices together, we will take the dot product of each row of the first matrix with each column of the second matrix. The position of the resulting entries will correspond to the row number and column number of the row and column vector that were used to find that scalar. Lets look at an example to make this more clear.\n",
        "\n",
        "![Dot Product Matrix Multiplication](https://www.mathsisfun.com/algebra/images/matrix-multiply-a.svg)\n",
        "\n",
        "\\begin{align}\n",
        "\\begin{bmatrix}\n",
        "1 & 2 & 3 \\\\\n",
        "4 & 5 & 6\n",
        "\\end{bmatrix} \n",
        "\\times\n",
        "\\begin{bmatrix}\n",
        "7 & 8 \\\\\n",
        "9 & 10 \\\\\n",
        "11 & 12\n",
        "\\end{bmatrix} \n",
        "=\n",
        "\\begin{bmatrix}\n",
        "(1)(7)+(2)(9)+(3)(11) & (1)(8)+(2)(10)+(3)(12)\\\\\n",
        "(4)(7)+(5)(9)+(6)(11) & (4)(8)+(5)(10)+(6)(12)\n",
        "\\end{bmatrix}\n",
        "=\n",
        "\\begin{bmatrix}\n",
        "(7)+(18)+(33) & (8)+(20)+(36)\\\\\n",
        "(28)+(45)+(66) & (32)+(50)+(72)\n",
        "\\end{bmatrix}\n",
        "=\n",
        "\\begin{bmatrix}\n",
        "58 & 64\\\\\n",
        "139 & 154\n",
        "\\end{bmatrix}\n",
        "\\end{align}"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "aJt-S8zA_Lk9"
      },
      "source": [
        "## Transpose\n",
        "\n",
        "A transposed matrix is one whose rows are the columns of the original and whose columns are the rows of the original.\n",
        "\n",
        "Common notation for the transpose of a matrix is to have a capital $T$ superscript or a tick mark:\n",
        "\n",
        "\\begin{align}\n",
        "B^{T}\n",
        "\\qquad\n",
        "B^{\\prime}\n",
        "\\end{align}\n",
        "\n",
        "The first is read \"B transpose\" the second is sometimes read as \"B prime\" but can also be read as \"B transpose\".\n",
        "\n",
        "The transpose of any matrix can be found easily by fixing the elements on the main diagonal and flipping the placement of all other elements across that diagonal.\n",
        "\n",
        "<center>![Matrix Transpose](http://xaktly.com/Images/Mathematics/MatrixAlgebra/MatrixOperations/MatrixTranspose.png)\n",
        "  \n",
        "\\begin{align}\n",
        "  B = \n",
        "\\begin{bmatrix}\n",
        "  1 & 2 & 3 \\\\\n",
        "  4 & 5 & 6\n",
        "\\end{bmatrix}\n",
        "  \\qquad\n",
        "  B^{T} = \n",
        "  \\begin{bmatrix}\n",
        "  1 & 4 \\\\\n",
        "  2 & 5 \\\\\n",
        "  3 & 6\n",
        "  \\end{bmatrix}\n",
        "\\end{align}"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "dDTzd-Mw_Q0G"
      },
      "source": [
        "## Square Matrix:\n",
        "\n",
        "In a true linear algebra class after the first few weeks you would deal almost exclusively with square matrices. They have very nice properties that their lopsided sisters and brothers just don't possess. \n",
        "\n",
        "A square matrix is any matrix that has the same number of rows as columns:\n",
        "\n",
        "\\begin{align}\n",
        "A =\n",
        "\\begin{bmatrix}\n",
        "  a_{1,1}\n",
        "\\end{bmatrix}\n",
        "\\qquad\n",
        "B =\n",
        "\\begin{bmatrix}\n",
        "b_{1,1} & b_{1,2} \\\\\n",
        "b_{2,1} & b_{2,2}\n",
        "\\end{bmatrix}\n",
        "\\qquad\n",
        "C =\n",
        "\\begin{bmatrix}\n",
        "c_{1,1} & c_{1,2} & c_{1,3} \\\\\n",
        "c_{2,1} & c_{2,2} & c_{2,3} \\\\\n",
        "c_{3,1} & c_{3,2} & c_{3,3} \n",
        "\\end{bmatrix}\n",
        "\\end{align}"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "fSfLokfx_T4x"
      },
      "source": [
        "### Special Kinds of Square Matrices\n",
        "\n",
        "**Diagonal:** Values on the main diagonal, zeroes everywhere else.\n",
        "\n",
        "\\begin{align}\n",
        "A =\n",
        "\\begin{bmatrix}\n",
        "a_{1,1} & 0 & 0 \\\\\n",
        "0 & a_{2,2} & 0 \\\\\n",
        "0 & 0 & a_{3,3} \n",
        "\\end{bmatrix}\n",
        "\\end{align}\n",
        "\n",
        "**Upper Triangular:** Values on and above the main diagonal, zeroes everywhere else.\n",
        "\n",
        "\\begin{align}\n",
        "B =\n",
        "\\begin{bmatrix}\n",
        "b_{1,1} & b_{1,2} & b_{1,3} \\\\\n",
        "0 & b_{2,2} & b_{2,3} \\\\\n",
        "0 & 0 & b_{3,3} \n",
        "\\end{bmatrix}\n",
        "\\end{align}\n",
        "\n",
        "**Lower Triangular:** Values on and below the main diagonal, zeroes everywhere else.\n",
        "\n",
        "\\begin{align}\n",
        "C =\n",
        "\\begin{bmatrix}\n",
        "c_{1,1} & 0 & 0 \\\\\n",
        "c_{2,1} & c_{2,2} & 0 \\\\\n",
        "c_{3,1} & c_{3,2} & c_{3,3} \n",
        "\\end{bmatrix}\n",
        "\\end{align}\n",
        "\n",
        "**Identity Matrix:** A diagonal matrix with ones on the main diagonal and zeroes everywhere else. The product of the any square matrix and the identity matrix is the original square matrix $AI == A$. Also, any matrix multiplied by its inverse will give the identity matrix as its product.  $AA^{-1} = I$\n",
        "\n",
        "\\begin{align}\n",
        "D =\n",
        "\\begin{bmatrix}\n",
        "  1\n",
        "\\end{bmatrix}\n",
        "\\qquad\n",
        "E =\n",
        "\\begin{bmatrix}\n",
        "1 & 0 \\\\\n",
        "0 & 1\n",
        "\\end{bmatrix}\n",
        "\\qquad\n",
        "F =\n",
        "\\begin{bmatrix}\n",
        "1 & 0 & 0 \\\\\n",
        "0 & 1 & 0 \\\\\n",
        "0 & 0 & 1 \n",
        "\\end{bmatrix}\n",
        "\\end{align}\n",
        "\n",
        "**Symmetric:** The numbers above the main diagonal are mirrored below/across the main diagonal.\n",
        "\n",
        "\\begin{align}\n",
        "G =\n",
        "\\begin{bmatrix}\n",
        "1 & 4 & 5 \\\\\n",
        "4 & 2 & 6 \\\\\n",
        "5 & 6 & 3 \n",
        "\\end{bmatrix}\n",
        "\\end{align}\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "rBwAaji5San4"
      },
      "source": [
        "## Determinant\n",
        "\n",
        "The determinant is a property that all square matrices possess and is denoted $det(A)$ or using pipes (absolute value symbols) $|A|$\n",
        "\n",
        "The equation given for finding the determinant of a 2x2 matrix is as follows:\n",
        "\n",
        "\\begin{align}\n",
        "A = \\begin{bmatrix}\n",
        "a & b \\\\\n",
        "c & d\n",
        "\\end{bmatrix}\n",
        "\\qquad\n",
        "|A| = ad-bc\n",
        "\\end{align}\n",
        "\n",
        "The determinant of larger square matrices recursively by finding the determinats of the smaller matrics that make up the large matrix.\n",
        "\n",
        "For example:\n",
        "\n",
        "<center><img src=\"https://wikimedia.org/api/rest_v1/media/math/render/svg/14f2f2a449d6d152ee71261e47551aa0a31c801e\" width=500></center>\n",
        "\n",
        "The above equation is **very** similar to the equation that we use to find the cross-product of a 3x3 matrix. The only difference is the negative sign in front of the $b$. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "8aGG5d4HSauH"
      },
      "source": [
        "## Inverse\n",
        "\n",
        " There are multiple methods that we could use to find the inverse of a matrix by hand. I would suggest you explore those methods --if this content isn't already overwhelming enough. The inverse is like the reciprocal of the matrix that was used to generate it. Just like $\\frac{1}{8}$ is the reciprocal of 8, $A^{-1}$ acts like the reciprocal of $A$.  The equation for finding the determinant of a 2x2 matrix is as follows:\n",
        " \n",
        " \\begin{align}\n",
        "A = \\begin{bmatrix}\n",
        "a & b \\\\\n",
        "c & d\n",
        "\\end{bmatrix}\n",
        "\\qquad\n",
        "A^{-1} = \\frac{1}{ad-bc}\\begin{bmatrix}\n",
        "d & -b\\\\\n",
        "-c & a\n",
        "\\end{bmatrix}\n",
        "\\end{align}"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "tlOXGq4QMSZy"
      },
      "source": [
        " ### What happens if we multiply a matrix by its inverse?\n",
        "\n",
        "The product of a matrix multiplied by its inverse is the identity matrix of the same dimensions as the original matrix. There is no concept of \"matrix division\" in linear algebra, but multiplying a matrix by its inverse is very similar since $8\\times\\frac{1}{8} = 1$. \n",
        "\n",
        "\\begin{align}\n",
        "A^{-1}A = I \n",
        "\\end{align}\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "46cJIv0YL7Jp"
      },
      "source": [
        "### Not all matrices are invertible\n",
        "\n",
        "Matrices that are not square are not invertible.\n",
        " \n",
        " A matrix is invertible if and only if its determinant is non-zero. You'll notice that the fraction on the left side of the matrix is $\\frac{1}{det(A)}$.\n",
        " \n",
        " As you know, dividing anything by 0 leads to an undefined quotient. Therefore, if the determinant of a matrix is 0, then the entire inverse becomes undefined. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "Iq0TYH-jMBwK"
      },
      "source": [
        "### What leads to a 0 determinant?\n",
        " \n",
        " A square matrix that has a determinant of 0 is known as a \"singular\" matrix. One thing that can lead to a matrix having a determinant of 0 is if two rows or columns in the matrix are perfectly collinear. Another way of saying this is that the determinant will be zero if the rows or columns of a matrix are not linearly dependent. \n",
        " \n",
        "One of the most common ways that a matrix can end up having rows that are linearly dependent is if one column a multiple of another column. Lets look at an example:\n",
        "\n",
        "\\begin{align}\n",
        "C =\\begin{bmatrix}\n",
        "  1 & 5 & 2 \\\\\n",
        "  2 & 7 & 4 \\\\\n",
        "  3 & 2 & 6\n",
        "\\end{bmatrix}\n",
        "\\end{align}\n",
        "\n",
        "Look at the columns of the above matrix, column 3 is exactly double column 1. (could be any multiple or fraction) Think about if you had some measure in a dataset of distance in miles, but then you also wanted to convert its units to feet, so you create another column and multiply the mile measure by 5,280 (Thanks Imperial System). But then you forget to drop one of the columns so you end up with two columns that are linearly dependent which causes the determinant of your dataframe to be 0 and will cause certain algorithms to fail. We'll go deeper into this concept next week (this can cause problems with linear regression) so just know that matrices that have columns that are a multiple or fraction of another column will cause the determinant of that matrix to be 0.\n",
        " \n",
        " For more details about when a matrix is invertible google the \"Invertible Matrix Theorem\" but be prepared for some heavy linear algebra jargon."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "aLj9XAZHQgSP"
      },
      "source": [
        "## Who's ready to get familiar with NumPy???\n",
        "\n",
        "[Helpful NumPy Linear Algebra Functions](https://docs.scipy.org/doc/numpy-1.15.1/reference/routines.linalg.html)\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "UVhixZZZQfUw",
        "colab": {}
      },
      "source": [
        "\n",
        "### What should we do first? :) Want to see anything demonstrated?"
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}