\\n\",\n \" \\n\",\n \" \\n\",\n \" \"\n ]\n },\n \"metadata\": {},\n \"execution_count\": 136\n }\n ],\n \"source\": [\n \"### ENTER CODE HERE ###\\n\",\n \"data = pd.read_csv('./2D_data.csv')\\n\",\n \"data.describe()\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"6EmCze5emem-\"\n },\n \"source\": [\n \"# Plot Initial Data\\n\",\n \"\\n\",\n \"Begin by specifying the `colors`, `sizes`, and `limits` parameters for the `plotTransformedData` function. You will not call the `plotTransformedData(original_df, trans_df, colors, size, limits)` function in this section, but rather you'll invoke it below in the section called _Perform Linear Transformations and Plot Results_. However, you will plot the `data` DataFrame here, merely to inspect it, using the marker colors, marker sizes, and axis limits specified by the `colors`, `sizes`, and `limits` parameters.\\n\",\n \"\\n\",\n \"So, plot `data` here. You should emulate the marker colors and sizes shown below as best as you can. The marker sizes range from small to large, and the marker colors vary from black to red. \"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 137,\n \"metadata\": {\n \"colab\": {\n \"base_uri\": \"https://localhost:8080/\",\n \"height\": 319\n },\n \"id\": \"4BPk10S6menH\",\n \"outputId\": \"c74eb9b5-3689-4300-ded9-d7bc30cc508d\"\n },\n \"outputs\": [\n {\n \"output_type\": \"execute_result\",\n \"data\": {\n \"text/plain\": [\n \"(-2.25, 2.25)\"\n ]\n },\n \"metadata\": {},\n \"execution_count\": 137\n },\n {\n \"output_type\": \"display_data\",\n \"data\": {\n \"text/plain\": [\n \"
\"\n ],\n \"image/png\": 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\\n\"\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n }\n }\n ],\n \"source\": [\n \"from matplotlib.colors import LinearSegmentedColormap\\n\",\n \"import matplotlib.colors as mcolors\\n\",\n \"\\n\",\n \"n = data.shape[0]\\n\",\n \"\\n\",\n \"def to_frac(x):\\n\",\n \" return np.interp(x=x,xp=[0,255],fp=[0,1])\\n\",\n \"\\n\",\n \"cdict = {\\n\",\n \" 'red':((0.0, to_frac(0),to_frac(0)),\\n\",\n \" (1/5*1,to_frac(51),to_frac(51)),\\n\",\n \" (1/5*2,to_frac(102),to_frac(102)),\\n\",\n \" (1/5*3,to_frac(153),to_frac(153)),\\n\",\n \" (1/5*4,to_frac(204),to_frac(204)),\\n\",\n \" (1.0,to_frac(255),to_frac(255))),\\n\",\n \" \\n\",\n \" 'green':((0.0, to_frac(0), to_frac(0)),\\n\",\n \" (1/5*1, to_frac(0), to_frac(0)),\\n\",\n \" (1/5*2, to_frac(0), to_frac(0)),\\n\",\n \" (1/5*3, to_frac(0), to_frac(0)),\\n\",\n \" (1/5*4, to_frac(0), to_frac(0)),\\n\",\n \" (1.0, to_frac(0), to_frac(0))),\\n\",\n \" \\n\",\n \" 'blue': ((0.0, to_frac(0), to_frac(0)),\\n\",\n \" (1/5*1, to_frac(0), to_frac(0)),\\n\",\n \" (1/5*2, to_frac(0), to_frac(0)),\\n\",\n \" (1/5*3, to_frac(0), to_frac(0)),\\n\",\n \" (1/5*4, to_frac(0), to_frac(0)),\\n\",\n \" (1.0, to_frac(0), to_frac(0))),\\n\",\n \"}\\n\",\n \"\\n\",\n \"mycmap = mcolors.LinearSegmentedColormap(\\\"Custom\\\", cdict, N=n)\\n\",\n \"colors = [mcolors.rgb2hex(mycmap(i)) for i in range(mycmap.N)]\\n\",\n \"\\n\",\n \"sizes = np.linspace(10,100,n)\\n\",\n \"\\n\",\n \"limits = np.array([-2.25, 2.25, -2.25, 2.25])\\n\",\n \"\\n\",\n \"data.plot.scatter(x = 'x',y='y', title='2D Data', c=colors, s=sizes )\\n\",\n \"plt.xlim(limits[0], limits[1])\\n\",\n \"plt.ylim(limits[2], limits[3])\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"cYbPudh8menL\"\n },\n \"source\": [\n \"# Define Data Matrix and Transformation Matrices\\n\",\n \"\\n\",\n \"Create a NumPy array called `X` from the `data` DataFrame above. Further, you must define the following transformation matrices. You must declare these matrices to be NumPy arrays, and name them A1, A2, ..., AN, as shown.\\n\",\n \"\\n\",\n \"\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 138,\n \"metadata\": {\n \"id\": \"6NVwkYXZmenM\"\n },\n \"outputs\": [],\n \"source\": [\n \"# -------------------- Define X NumpPy Array -------------------- #\\n\",\n \"\\n\",\n \"# Data Matrix\\n\",\n \"### ENTER CODE HERE ###\\n\",\n \"X = data.to_numpy()\\n\",\n \"\\n\",\n \"# -------------------- Define 13 NumPy Arrays -------------------- #\\n\",\n \"k = 0.5\\n\",\n \"m = 0.5\\n\",\n \"c = 2.0\\n\",\n \"r = 0.5\\n\",\n \"phi = np.pi/4\\n\",\n \"### ENTER CODE HERE ###\\n\",\n \"A1 = np.array([[-1, 0],[0, -1]])\\n\",\n \"A2 = np.array([[k, 0],[0,1]])\\n\",\n \"A3 = np.array([[np.cos(phi), -1*np.sin(phi)], [np.sin(phi), np.cos(phi)]])\\n\",\n \"A4 = np.array([[-1, 0],[0, 1]])\\n\",\n \"A5 = np.array([[1, 0],[0, c]])\\n\",\n \"A6 = np.array([[1, 0],[r, 1]])\\n\",\n \"A7 = np.array([[1, m],[0, 1]])\\n\",\n \"A8 = np.array([[0, -1],[-1, 0]])\\n\",\n \"A9 = np.array([[1, 0],[0, 0]])\\n\",\n \"A10 = np.array([[0, 0],[0, 1]])\\n\",\n \"A11 = np.array([[1, 0],[0, -1]])\\n\",\n \"A12 = np.array([[0, 1],[1, 0]])\\n\",\n \"A13 = np.array([[1, 0],[0, 1]])\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"j1FVev5zmenS\"\n },\n \"source\": [\n \"# Perform Linear Transformations and Plot Results\\n\",\n \"\\n\",\n \"In this section, you will perform the following:\\n\",\n \"\\n\",\n \"$$\\n\",\n \"\\\\mathbf{X}_{trans} = \\\\mathbf{A} \\\\mathbf{X}^T\\n\",\n \"$$\\n\",\n \"\\n\",\n \"where $\\\\mathbf{X}$ is the data you read in from the file, $\\\\mathbf{A}$ is any one of the thirteen transformation matrices, and $\\\\mathbf{X}_{trans}$ is the transformed data. You should express the matrix multiplication in one line of code! \\n\",\n \"\\n\",\n \"**Important:** When performing the matrix multiplication, please note that the order in scalar or dot product matters. A dot B is not the same as B dot A.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"xydZ3jQ8menT\"\n },\n \"source\": [\n \"### Identity Matrix\\n\",\n \"\\n\",\n \"Any matrix $\\\\mathbf{A}$ multiplied by the ___Identity Matrix___ $\\\\mathbf{I}$ is equal to itself! That is, $\\\\mathbf{AI} = \\\\mathbf{A}$. The 2D identity matrix is given below. \"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 139,\n \"metadata\": {\n \"colab\": {\n \"base_uri\": \"https://localhost:8080/\",\n \"height\": 411\n },\n \"id\": \"Aw3lewOemenW\",\n \"outputId\": \"889676b7-2d04-46a9-a207-e402e41ce52e\"\n },\n \"outputs\": [\n {\n \"output_type\": \"display_data\",\n \"data\": {\n \"text/plain\": [\n \"
\"\n ],\n \"image/png\": 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AAAAAADyERAAAAAOAhJAIAAAAAPIREAAAAAICHkAgAAAAA8BASAQAAAAAeQiIAAAAAwENIBAAAAAB4CIkAAAAAAA8hEQAAAADgISQCAAAAADyERAAAAACAh5AIAAAAAPAQEgEAAAAAHkIiAAAAAMBDSAQAAAAAeAiJAAAAAAAPIREAAAAA4CEkAgAAAAA8hEQAAAAAgIeQCAAAAADwEBIBAAAAAB5CIgAAAADAQ0gEAAAAAHgIiQAAAAAADyERAAAAAOAhJAIAAAAAPIREAAAAAICHkAgAAAAA8BASAQAAAAAeQiIAAAAAwENIBAAAAAB4CIkAAAAAAA8hEQAAAADgISQCAAAAADyERAAAAACAh5AIAAAAAPAQEgEAAAAAHkIiAAAAAMBDSASwVXLOqXTSJK144AGtfOQRVf7wQ9MKxmLSW29JAwdKubnxj4EDpTffjB8DAGALUV1crNVjxmjFffdp7SuvKFZZ2bSCK1ZIt9wi9eghBQJS167SNddICxY0S79oeW0yJJrZ5WZWaGZVZjamkbVXm9kKMysxs2fMLLuF2gR+ttavWKE5H3+sVT/91Cz1Fr33nl4/9FA91bGjxvbsqSm33qrKtWvTrlc+bZq+2WknzR00SEuuv16L//hHfbv33przq1+pes2a1AuGw9KgQdLZZ0uffSZVVMQ/PvtMGjo0fiwcTrtfIFnMR6Bti8ViWvDVV5r76aeqqqhocr3KtWs1deRIje3ZU0917KjXDz1UC8ePT7uei8W0+Npr9XWPHlp4+eVacuONmn/BBZretauKnnoqvaKTJ0t9+0r33CMtXy5VVkpFRdLo0dKee0rvvpt2v2g95pxr7R42YWanSYpJOlZSwDl3Xj3rjpU0VtKRkpZJel3SF865GxqqX1BQ4AoLC5u1Z6CtCofD+vjtt7Vi8WIdcOSR2nWvvdKuFams1NPnn69pr72mzJwcVYfD6r3//rrs1VfVvlu3tGp+OWKEZjzwgKrLy73X/NnZyu7USb8uLFRu9+4p1Qt9951mDxigWFnZJscsK0vZO+2kftOny5eTk3zR3/1Oeu45KRSq+3ggEA+LTz6ZUq9oGWY2zTlX0Np9NIfNPR8lZiR+XpYtXKiP3npL7Tp00JGnnKLcvLy0a/3w+ed67IwzVLF+vXw+n2LRqIb8+c86+ve/T6texYoVeqWgQJVr1iha40pfRjCova+6Sgf++c8p11xw+eVa849/KFZHgPUFg+r58MPqcv75yRdcsULadVeptLT+NcGgNG2atNtuKfeLzauh+dgmQ+IGZnaHpO0bGIL/lLTAOXdT4uujJL3gnNu2oboMQPxclK5fr7MOOEArly1TdTgsn8+nC2+6SRePGJFWvSfPPVdTX3lFkRphyZeRoR67765RM2bIzFKqVzR9ul4fOFDVdQwry8hQrxNP1Amvv55SzR9OOUXr3nxTqudnmy83V71Gj1bn885LruCaNdL228fPjDYkJ0daskTq1CmlfrH5bU0hcYPNNR8lZiR+Pt57+WXdlJgFfr9f2YGAXpoyRdv17p1yreKlS3Vj376qqnHCU5KygkFdOHasCoYMSbnm+NNO04K33pKrrt7kWEYwqFM/+URd9t8/6XpVixZpZt++cg3MM3/79tq3qEi+zMzkit5yS/wKYkMz0u+Xzj1XevrppHtFy2hoPrbJ7aYp6CdpRo2vZ0jqZmab/JZmZhcltugUFhUVtViDQGt6/qGHtHTBAlWUlipcVaXKUEiP33GHVi1blnKtsrVrNfXllzcKiJIUq65W0fz5mjd5cso1Z44erWhVVZ3HXHW1Fo8fr8ri4qTrRUtLtf699+oNiJIUKy/XygcfTL7JV1+VfEn8qPT54muBtiHp+SgxI/HzEw6HdeuFF6oqFFJVKKSKsjKtX7NG9153XVr1Pvr73xWtI8yFKyr0xsiRKderWrdOi959t86AKEnRqirNHD06pZqrn322wfkoxe/nL3nvveSLPvVU4ydRo1Hpn/9s9M9G27Klh8Q8SetrfL3h8/zaC51zTzjnCpxzBV26dGmR5oDWNuWjjxSuFcKysrM15+uvU65V9NNPysjKqvugc1r+3Xcp11w3Z45cNFrvcV9WlipSCLTVq1fLMjIaXRdevjzpmlq1qv5tpjWFQtLKlcnXBTavpOejxIzEz8/yRYsUrTV/YrGYvk7jhKckLfzqK1XXc9Kz6McfU65XvmyZfPXNXEkuGlXxnDkp1QwvWCBXT49e3UhE4aVLky+a7IncSKTxMIk2ZUsPiWWS2tX4esPnDWyMBn4+9howQJm1hkwkHFafPfZIuVbHHXZQpJ7hYj6fOu+4Y8o183v3lhrYohoLhxXo2jXpev6OHeUikUbXZaSyJbRjx/hW0sbk5MTXAm0D8xFoQLftttvkNTNT3733Tqte9913l7+eLZrb1PFnNSbQtatiDT0QzUztUtwWm9mjh9TINlLLyFBGCnNX+XWed9qUz5fcLEWbsaWHxFmS9qnx9T6SVjrn0nh8IbD1OfcPf1CHTp2UEwxKkgK5uTrtggvSut+ifbdu2uvYY5WRvfEDEs3nU16nTtrt8MNTrrnnpZcqIxCo85j5fOo+cKACKVzVyGjfXvmHHtrgGl8wqK6XXpp8k6eemtxbXMRi0mmnJV8X2LyYj0ADcgIBXXP33coJBmU+n7KysxXMy9M1d9+dVr0jL7lE/jp2smQFgzrhxhtTrhfo3Fndf/lLWT23O2QEg9ozlVkmqfM55zS+28Y5dTj++OSLDhsmNXDFU1I8IJ56aoMnhdH2tMmQaGYZZpYjyS/Jb2Y5ZlbXf9VjJV1gZnuYWQdJIySNacFWgTatU9euenvOHP3xnns0/NprNXrcOP3p4YfTrnfhc8+pz0EHKSsQUE5+vrLz8tS1Tx9d+9//ypfMfXu1bHvwwdr5zDOVkQixG5jfr6z27XXY44+nXHP7v/5Vvlr1PH6//B07qvOwYckX7N5dOvnkhs+A5uRIJ50UXwtsRsxHoPmcdemlGjtpki647jpdcfvtemfuXO3cr19atbr26aNLX3lFOe3axT/y85WZk6OjLrtMvxw+PK2ahz3+uLI6dNgk2GXk5mrn3/xG2x5ySEr1cnbdVR1OOklWz8lZXzCoHjffLF89x+t0xRWNXp1UTo50Q6MPVkYb0yafbmpmIyXdWuvl2yQ9I2m2pD2cc4sSa/8g6XpJAUmvSrrYOdfghmue3AY0zdJZs7R01ix13GEH9TnwwJSfalqTc07fP/uspt15p0rmzZM/ENAuZ56pgltuUX7PnmnVXD9hgn789a/lqqvjb4VhJl8wqKzevbXr+PHK3mGH1AqWl0uHHy7Nnh1/f8SagkFp992ljz+WcnPT6heb19b0dNPNPR8lZiTQFJGqKs3+738VrqhQ30MPVbtUtm7WoXTxYhWOGqUfXnxR0VBI7fr00S9uukl9zz03rdkbC4c1f/hwFb/2mhSLyYXD8dDonLrfcIN63HJL6nXHj5dOP12qqoo/pGaDDVtMH3ssfsURbc4W+xYYmwsDENj6xcJhrXvjDZVNnSpfVpbaDxqkvIMOSj/QVlVJzz4bf9T3hocQ7LSTdO210nnnSdm8T3lbtTWFxJbAjAS2flULFmjNv/6l6lWrlL3jjup09tmp3a9f2/ffS3ffHX+KaSTyvy2mN9wg7bdf8zWOZkVIrIUBCKBJNjwcJ9n3kUKrIiSmhhkJIG3OxZ9impPDPYhbgIbmY+PPigcAbIxwCADApsykVO5pRJvVJh9cAwAAAABoHYREAAAAAICHkAgAAAAA8BASAQAAAAAeQiIAAAAAwENIBAAAAAB4CIkAAAAAAA8hEQAAAADgISQCAAAAADyERAAAAACAh5AIAAAAAPAQEgEAAAAAHkIiAAAAAMBDSAQAAAAAeDJauwEA2FxiVVWqXLBAlpmpnB13lJk1qZ4rLlZkzBjFPvxQkuQ74ghlDh8u22ab5mgXAIAWE165UpG1a5W17bbKbOIcc84pNnWqqp96Sm7RIlm3bsoYPly+ww5r8uxF6yAkAmh14bIyzX7hBS2bPFmBzp3Vb9gwdd1777TrRcvL9dOIEVrx1FOSJBeLKbNjR/W6+WZ1v/DCtAZW5OmnFb7iCslMqqiI/zkffqjIn/6krIcfVub//V/a/QIAUJ9V33yjWc89p1BRkXocdJD2GDpUWXl5addb/9lnmnfNNSr7+mv5srIUC4fV8eij1ee++xTcZZeU67niYlUOGqTYjBlSZaUUi0lmqn7tNVmvXsr5z3/k69Ej7X7ROsw519o9tLiCggJXWFjY2m0ALSYWiylUUaHcJgyVDb6ZMEEv3nSTlsyerW26d9epN92kw887L+0zhcu+/FKvHHusXHW1IuXlMr9f/qws7XbmmTruqadkvtR2xUdDIX110EGq+P57ucrKjY75gkF1v/BC7fLAAynVjLz8ssLDh3vhcBPBoLKeflqZZ56ZUl20DDOb5pwraO0+thTMSPzchCoqlJmVpYyMpl07qaqo0L9HjdJHzzyjSGWl9j7mGA296y5t26dPWvVcLKb3L7xQ3734oqLhsFw0qszcXFlGhn79/vvqccABKddcM368Zg0ZolgotPEBM/nbtdP+kycrd/fdk++xulqh/v3lZs+WwuFNF2RkyLbbToFZs2S5uSn3i82rofnIPYnAVu7FJ57Q7sGg9tlmGx2x665a9NNPadeaOm6c7h48WD9Onaqq8nKtmDdPz1x+uV4ZOTKteuGyMr1y7LEKr1+vSHm5JMlFo6oOhTTnpZf01ejRKddc8tBDCs2du0lAlKRYRYWWP/GESqdPT7qei8UU+f3v6w+IklRRofDVV8vFYin3CwBoHevWrtWQQw7RXu3aabdAQHfdcIPSvXgSi8V02xFH6N0HH1RJUZFCpaWa8vrruqGgQKsXL06r5lePPKI5//qXqkMhuWhUkhQpL1d4/fr47CwrS63HSETfDR26aUCUJOcULSnRnOHDU6oZfestuXnz6g6IklRdLbd6tSJjx6ZUF62PkAhsxaZ9/rlGXX21wlVVilZXa9GPP+qco49Oawg65zTmqqsUrhWWqioqNO7uu1VRUpJyzdkvvCBXXV3nseqKCn3517+m3OvSBx6oewAmxMJhLXnwwaTrxSZNkksE2AaVlys2cWLSdQEAreuqoUM1s7BQ0WhU0epqPfvww3r12WfTqvXNBx9oyezZitQ4QeliMVWVl2vcXXelXM85py/vvFORek5QuupqzX7++ZRqrnn77XpnbuIPVfk336hi3ryka0buv19qLKyWl6v6/vuTrom2gZAIbMWmTJqkSFWV93UsFtPyJUu0vrg45VqVZWVau2RJnccysrO1cMaMlGsu/+IL7wpiXUJFRQ0ery0WiSi8cmXDi6JRlX39dfI1f/wxfn9FowtjijXhKi0AoGVNmTRJkRpXwEIVFZo4fnxateZ8+qkq6whL0UhEMydMSLledSikilWr6j0eKS/Xsi++SKlmxZw5ijYyUy0rSxVz5iRd0/34Y3Lr6vn9AW0XIRHYim3TubOysrM3es05p9z8/JRrZebkyFfP/RrRSETtunRJuWZO584yv7/+BWbKyMlJup5lZDRcLyGjXbvkawaDUjL3Rfp88bUAgC1Cuw4dNvran5Ghrt27p1WrfdeuygoE6j7WrVvK9fzZ2Q3ek29+vwKdO6dWMy9PlpXV8CLn5E/l+QX1/J03Uet3EbR9hERgK3bK0KHarlcv5QQCMjMFgkFdd+edyszMTLlWRmamBp59tjJr/aD3+f3qvssu2m633VKu2e+cc+SvZ2CZz6edTz653mBa5/eYqeMJJ8SfQFoPX16etj3//KRr+o8+WopEGl8YDsfXAgC2CLc/9phygkH5fD5lZWerQ8eOuvj669OqdciZZ9Y5e7JzczXo6qtTrufz+7XzySfXGxT9WVnqN2xYSjU7Dx6sRh8xZ6b2Bx+cdE3/b37TeAD0+5UxeHDSNdE2EBKBrVhOIKA3Cwt109/+pitvuUVPjBunC6+5Ju16wx98ULsceKCygkFl5+YqJz9fXXr10nXjxqVVr+vee2v3s89WRq0rcObzKat9ex12990p1+w9cqR89Z3Z9PmUkaXwgfsAACAASURBVJ+vrr/5TdL1rHNn+QcPbngIZmfLP3iwLI2rqQCA1nH0ySfr5UmT9Ptbb9W1f/mL3v/227SvJLbr0kV/fO015eTlKZCfr5y8PGXm5Oj4K69U/zQD0mH33KOs9u03CYoZwaB2P+uslN8qKqdnT3UaPLjeGekLBtVrxAj5GrvaWEPmJZdIje3gyc5W5h/+kEqraAN4CwwAKZs/fboWzpihzr16aY/DDpMvxbepqMnFYpr+6KP64s47VbFqlcxMOw8erMPuuksddtoprZpr3nlHsxJBMJa4/8Kfn6+Mjh2174cfKpBiXVdSotBBB8n99FP8PaBqysmR7bSTApMny1LYxoqWw1tgpIYZCaSvqqJCX7/3nqrKy7XnUUepYxPfH3Dd/Pn6+LrrNG/cODnnFOzSRQfceKP2v+yylN8iSpKilZWafcYZKv7vfxWrqpKiUVlWlszn03ZXXKGd7ror5be0irz2msLnnCOFQlLtXBEMKuvee5V58cUp94rNr6H5SEgE0CY45xSpqFBGdnZKW0zrU11aqpUvvKD1n3wiX3a2ugwZoo7HHZfUPYt19ldersj99yvy4IPShhv/c3OVeeWVyvzDH3j/pzaMkJgaZiTQ9sSqq1VdVaXMYDDt9yWuqeybb7RizBhVLVum4K67qvsFFyinV6+060WnTlVk5EhFJ0yQMjOlSES+gw9W1q23yn/44U3uF5sHIbEWBiCAdLloVC7xBFXr1i3t0ImWQ0hMDTMSQLpcWZnc2rWy9u1l7du3djtoREPzsemn6wHgZ8T8flkTtw8BALA1srw8WSpPR0WbxYNrAAAAAAAeQiIAAAAAwENIBAAAAAB4CIkAAAAAAA8hEQAAAADgISQCAAAAADyERAAAAACAh5AIAAAAAPAQEgEAAAAAHkIiAAAAAMBDSAQAAAAAeAiJAAAAAAAPIREAAAAA4CEkAgAAAAA8Ga3dAABsSarnzFH1l19KkjIOOEAZu+3Wyh0BAND6XDis8AcfKLZ8uXydOyvrmGNkwWBrt4U0tckriWbW0cxeN7NyM1toZmfXs26kmUXMrKzGx04t3S+ApitZulQ/jB+vxV98oVgs1uR6az/5RFNPOkkTunbVf7fbTt9ecYUqfvop7XrVc+eq+IADVLz//iq97DKVXnaZivffX8UHHKDquXOb3C+QLGYk8PMSi8W0+Isv9MP48SpZurTJ9SIlJZr/wAOa2LevPujcWZ/uv7+WPv+8YpFIWvWcc6q47z6t6dpVJWefrbKrrlLpsGFa3bWrykeMkGuGmY6WZ8651u5hE2b2ouIB9gJJ+0p6R9LBzrlZtdaNlLSzc+63qdQvKChwhYWFzdQt8PNSWV6uj55/Xt9Nnqztd9tNx5x/vjp07Zp2vaqyMr0+bJh+GD9eGdnZcrGYsnJzderYsepz9NFp1Zw7cqTm33OPoqGQlPgZZ5mZ8mVl6RdvvqnORx6ZUr3ovHkqLiiQKynx6nnMZO3aaZvCQvl33jmtfrF5mdk051xBa/fRXJiRQNu1YOZMfTBmjEKlpTpw8GAVHH+8fL70r8n8OGGCXj/nHIXLy2U+n6qrqrTL8cfr1LFjlZ2Xl3K9qhUr9NkBByi8erViFRXe6/7cXLXbd18NmDBB/pyclGqWXX+9Qo88IpWXb3owGFT2aacpf+xYmVnK/WLzamg+trmQaGa5kool7emcm5t47TlJS51zN9RaO1IMQKBBa9es0V233KIlCxfq+FNO0dALLkj7B3XxypW6qn9/la1dq8rycmXl5Mifmam7Pv5YffbbL62aY444QosnT1a0qmqj1zODQQ3/5BP12H//lOqt/vBDTTvpJEVrDL+a/Hl5OnLpUmW2a5d0zXVHH63Ihx9K9Z0N9fmUecQR6jBhQkq9omVsTSGRGQk0rw/eeUfPPfmk2rVvrz/eeqt675T+xfZ3HntMT11zjarDYcWiUeXk5WmfI47QiDfeSCsoLp8+Xc8MHKhIrXnmz87W9gceqOETJ6Zcc/Khh6p48mSpunqTY75AQD0vvlh73Hdf0vWqf/hBxfvsI4VC9S/KzVWH999X5iGHpNwvNq+G5mNb3G66q6TqDcMvYYakfvWsP8nM1prZLDO7ZPO3B2w5KisrdeyAAXr+ySf1wTvvaMRVV+mhv/417XpjbrxRxcuXqzJxtjBcWalQaanuPffctOot++orLZ0yZZOAKEmRUEgTR45MueaPd95Zb0CUJDmnpc89l3S96JIlinzySf0BUZJiMUU+/VTRJUtS6BRICzMSaCbvvvGG/u+MM/TeuHH69/PP6+hf/EIrV6xIq1bJmjV66g9/UDgUUiwalSRVlpVpxocf6otx49KqOXHkSEXqCF/RqiotmzpVy776KqV65T/8oPVTp9YZECUpFgpp8ZNPKlpZmXTN0EMP1VvPU1GhinvvTaVVtAFtMSTmSSqp9dp6Sfl1rH1Z0u6Suki6UNItZnZWXUXN7CIzKzSzwqKioubsF2izvp46VWuKihRJ3GdQUV6up0ePTrveF+PGKVrHMFj6/fcqXbs25XrzP/xQ0frugXBOC9I4S7p+ypQGj0fLy7UmhSt+0W+/lSWx9cZyclQ9c2bSdYE0MSOBZvLEgw8qlDipGIvFFA6HNeGdd9Kq9fWECfJnZm7yemV5uSa99FJaNRdMnLjpLQ4J0UhE8//735TqrfvyS1lGI8+sNFN5CvfZV3/+udTYvYzOqXrq1KRrom1oiyGxTFLtfWDtJJXWXuicm+2cW+acizrnPpf0oKTT6yrqnHvCOVfgnCvo0qVLszcNtEVZ2dmqvaU8Ozs77XqZWVl1H3CuzuHYGH9mpqyBLTi+xoZZnUX9jS7xpfJvkEQ9SZJzsmTXAuljRgLNJBAIbPS1mSkrzRmZmZNT560cZqbsNJ/w2dAMNJ9P/vpmcn3fk5EhNXa7iXONB8makp39zMctTlsMiXMlZZjZLjVe20fSrHrW1+QkcVcskLBvQYH2HzBAwdxcZWRkKBAI6Na//S3tekcPH66sWlfV/BkZ6nfooQrm13Uho2F9Tz653vsjLSNDe5xe5++zDep6wgkNhjV/fr62Pe20pOtl9O8vV8d22NpcOKyM/v2TrgukiRkJNJPrR41SMDdXmZmZCgSD2rZHD51w6qlp1dr/mGM2OSkrSVmBgI694IK0au4+ZEi9gc3M1Pfkk1Oq1+mII+TC4QbX+AMB5fXtm3TNrBNPlBrbbZORoazjjku6JtqGNhcSnXPlkl6TNMrMcs3sEEmDJW1yE5GZDTazbSxugKQrJaW38RvYCvl8Pr30/vu669FHdcMdd+j1iRN1YgoBqbazbrlFfQ88UNnBoLIDAQXy89WlZ09dM3ZsWvW22XFH7TNsmDJrnWU1n0/ZeXk6dMSIlGvudP31svrOBJspIy9P3U45Jel6vg4dlH366VJDZ2yzspQ9ZIh822yTYrdAapiRQPPZt6BA//3qK930l7/otnvv1YSvvlJubm5atbIDAd08bpxy8vIUyM9XdjCozOxsDbnuOu2R5gNbDh0xQtn5+ZvsuMkMBrX3b3+rbXbcMbUeu3XTtkOGyFdPqPMHg+pz000p7YoJXHRR41cnMzMVuOqqVFpFG9Dmnm4qxd8DStIzko6WtEbSDc65f5rZLyWNd87lJda9KOkYSdmSlkh61Dn3UGP1eXIbkD7nnOZOnaqfpk9Xtx131D5HHSV/E7aRxGIxfXb33fr8nnsUCYXkolH1PvxwnTB6tDrtskvjBeqw/LXXNOOcc6RYTLHEDfj+vDxl5OXpwEmTlJti3VhxsYr791ds8WKp9lnYrCz5tt9e2xQWEhLbqK3p6aYSMxJoy0JlZZry9tuqLCvTfscco649ezap3pp58/Tu5ZdrwUcfyfx+ZQYCOvjaa3XIddel9cTUaCikqYMGaf2UKfGHvDkn+f3yZWVp++HD1W/06JSfgB56/nmVXXRR3U84DQaVO2qUgtdck3Kv2Py2qLfAaAkMQKDtiUWjKl+1Sll5ecpOY+tqbVWrVmnxk09qzUcfyZeTox5nnqltf/1r+dO83yS2bp3Kb75Zlf/4h3eW1UWjyhk+XLm33y5fhw5N7hmbx9YWEjc3ZiTQ9lSVlipcVqbcrl3la+L9fc45FX/yiRY9/rgqly9XXt++6nXZZcrfc8+0a4Y//FDlN96o6m++kWVlyUUi8vfpo9w77lD24MFN6hebDyGxFgYggHS5UEjR77+XJPn79pXVevAB2h5CYmqYkQDSFV2yRLEVK+Tr1En+FLfDouU1NB/TeHQgAPx8WSCgjH33be02AABoc/zbby//9tu3dhtoBm3uwTUAAAAAgNZDSAQAAAAAeAiJAAAAAAAPIREAAAAA4CEkAgAAAAA8hEQAAAAAgIeQCAAAAADwEBIBAAAAAB5CIgAAAADAQ0gEAAAAAHgIiQAAAAAADyERAAAAAOAhJAIAAAAAPIREAAAAAICHkAgAKXCxmKIrVyq6cqVcLNba7QAA0GbEKipUvWSJYmVlrd0KmoiQCGCrFK2s1MLnn1fhRRdp+pVXatXEiXLOpV3PhcNaf889Wtyjh5b07q0lvXtrcY8eWnf33XLhcDN2DgDA5lX6ww/69uabNfX88zXn7rtVuXJlk+qFZ87UylNP1aJtttHSvn21qGNHrTjmGFV9+WUzdYyWZk35pWlLVVBQ4AoLC1u7DWCLtX71as3/9lttu+OO2rZXrybXmzVunN6/+WatnD1bWcGgfnHeeTrmttsU3GabtOqtnTJFk447Ti4SUXVZmWQmf26u8vr00WETJii7c+eU6rmqKq048kiFp0+XC4U2OmaBgLL220/bfvihLDs7rX6xeZnZNOdcQWv3saVgRgLpc87pxxkzFCorU9/+/ZXVxLlQUVys/9x6q6Y9+6zC5eXqtsceOmbUKO15yinp9ReL6atLLtGCsWPlolG5SES+nBxJ0t53361drrgi5ZqhiRO1atCg+HyslSssEFDn555T7pAhafWLzauh+ciVROBnYMH8+fr8009V1sTtH845PXHDDTpjhx004pRTdO5uu+nm005TuKoq7ZqfP/KI/nn22Voxc6ZcNKqq0lJ9+fjjerh/f1WWlqZcr3LFCn38q18pUlwcD4jxxhUtK1PJ7Nn65PjjU76iuO6OO1RVR0CUJBcKqWr6dBXffnvKvQIAWlc4HNaXkydr9qxZTa61YsECDdttN10xcKBuGDRIp3XtqsnvvJN2vaqyMj08YIC+fPxxVZWUyEWjWjFzpl4cOlSfjR6dVs3Zt9+uhc8/r1hlpVwkIkmKVVYqVlmpmTfcoGVvvZVSvVgopFWDB8tVVGwSEKX4jFx9zjmKFhWl1S9aDyER2Mo99fe/q6BfP50+aJD26tNHSxYvTrvWpFdf1eujRytcWany9esVrqzUlPfe05iRI9OqV1VWpneuu06RioqNXo+GwypZtkxTnnwy5ZrzHntMscTgq81FIir57jutTWH7i4tEVDJ6tFRHQPSEQip95BG2nQLAFqSsrEwH77efBh97rA4bMEDXXXVVk+rdeOKJWjZvnirLy1VRUqLykhLd9utfa+2KFWnV+/KJJ1SydKmitWZLpKJC715/vapSPPEbrazU3L/9TdFaM9c7XlGhb2++OaWaFS+/LCVxf35pGvMcrYuQCGzFotGorvv971UZCqmkpERr16zRXXfckXa9Nx55RJXl5Ru9Fg6F9O5TT6VV78ePPpIvI6POY5FQSIVjxqRcc8krryhWWVnv8WhFhZa//XbS9SLffy9VVze+MBqNrwUAbBGeHzNGC376SWWlpQpVVOjpxx/X4kWL0qq1eO5cLf/pJ8VqBSbnnD7+97/Tqjnt2WcVqecEpS8jQ/M+/DClesXTpkm+hn/1L5k9W5GSkqRrVrz1llwjYdWFQqp4882ka6JtICQCWzHnnKLRqPd1NBpVea2Ql4qqeoZVJM0raNFIpM7tKRsdT5FrLNA5V++VxrqbiDY6VCVJZkmdTQUAtA1VlZUbzUifz6dQQ7tGGhCpqpLP79/k9VgspnADJy4b0uAMTHWWKTEfzRpcY2aNz9HaNZNR498ZWwZCIrAVy8jI0P9dcolyc3MVCASUm5urK//wh7TrHXPOOcoOBjf+MzIz9ctTT02r3o4DB26yjWYDf3Z2Wjfmdz3qKFk9VyclKSM/X10OPTTpehk77ywlM4gjEWX06ZN0XQBA6zrj7LOV366dAsGgcvPydODBB2uXXXdNq1bvfv0UyM/f5HWfz6eDTz45rZr9Bg+Wv54H30QjEe34y1+mVK/9Pvso1sgzBLK7dVNmCg+Ny/nlL2W1fi/YRFaWsgcOTLom2gZCIrCV+9tDD+nZl17Snffdp8+//lr77r9/2rVOvOgi7XPoocrJzVVWTo4C+fnqvuOOuuRvf0urXl7Xrhpw4YXKrDVgzExZwaAOufLKlGvuevXV8mVm1n3QTJnt22vb445Lup4vN1e5Q4dK9dWUpMxM5Z59tnx5eSl2CwBoLd179NDUb7/VXfffr0eeekqvjx8va+RKW318Pp9Gvfqqgvn5CuTlKTsQUFZOjoaPGqUd0gyeA3//e2UFg5v0lBkMqv8FFyiva9eU6mV16KCeZ53lPc20Nn8wqN1vvDGlf4O84cMb3UVjPp/apfHUVLQu3gIDQEqcc5r9xReaO22aevTpo4JjjpG/ji02yYrFYpowapQ+ue+++PbYSETb/+IXOuMf/1CXNAfron/9S4Xnn69YNOo9TMafmyt/IKAjPvlE7XbbLaV60TVrtGz//RVdvnzTq4qZmfJvu616fPWV/Cm+tQZaBm+BkRpmJJC+itJSfTZunCpKS3XA8cdr2969m1SvaO5cvXz++VpSWCh/ZqbMTAOvvlpH33qrfMncClFLdUWFJh19tNZ/883/ngBuJn8wqB3OOEMFTz+dclAuffpprb3iijqfAG7BoNrfeKM6jBiRcq/Y/Bqaj4REAG1CdVWVihcuVKBDh5TPjtalfP58/fDww1r10UfyZ2er529/q97DhimzXbu06kWLirTm8stVMW6cLHEW1lVWKnjyyer0yCPyd+nS5J6xeRASU8OMBNqeslWrFFq3Ttv06qWMJr73ootGtfyddzTv0UdVuXy58vv21S5XXqlOhxyS9pXU8jfeUPE11yi6cqWUkSFFo/K1a6cOf/6z8s87r0n9YvMhJNbCAASQruiaNQpPny5JytpvP/k7dWrljtAYQmJqmJEA0uGcU3jGDEWXL5e/c2dl/eIXsjSudqLlNDQf63+6AwBgE/5OnRT41a9auw0AANoUM1P2vvtK++7b2q2gGRDvAQAAAAAeQiIAAAAAwENIBAAAAAB4CIkAAAAAAA8hEQAAAADgISQCAAAAADyERAAAAACAh5AIAAAAAPAQEgEAAAAAHkIiAAAAAMBDSAQAAAAAeAiJAAAAAAAPIREAAAAA4CEkAgAAAAA8hEQAW631c+dq3tix+ulf/1LV2rVNrlf+8cdaeMIJ+q5DB33XoYMWnnCCyj/+uBk6BQCg5UTDYS159139MGaMVkyaJOdc0+qtX6/V996ruTvtpO/y8/X9Djto1ahRqi4qaqaO0dIyWrsBAFi7aJE+vP9+zZ04UflduujQyy7T3iefLDNLq15lUZE+Ov10rZ4yRZaRIZnJRSLa5cILNeD+++Xz+1OuueLaa7X20UflQiEpMUzL3ntP5ZMmqeMll2jbe+5Jq1cAAOrjnNM3b76pSY88otKiIu1y2GE68uqr1alXr7Rrzn/pJU2++GK5WEwuGpXMlNWhgw5/5RV1PfDAlOuFFy3S/IMOUrS4OD4jJcXKyrT6zju19sEH1fuTT5Szxx5p94vW0SavJJpZRzN73czKzWyhmZ1dzzozs7vMbE3i4y5L97dKAEmZ8dlnOmuvvXSAz6cTd9hB7//zn02qt7CwUHfsuacmPfKIln79teZ88IHGDB2qseeem9aZzVgkoncHDtSqyZMVraxUdVmZqktLFa2s1A9PP60vr7wy5ZrrX3lFax97TK6iwguIkiTn5MrLtfaxx7T+lVdSrgukgxkJtE3VkYgeuvZaHZafr4MyM3XVoEFavXx52vWcc3pu+HCNGTpUcz74QEu//lqfPPqo/rzXXlo4dWpaNZeMH69Pzz9f4XXrFCkpUXV5uarLylSxZIn+86tfaf3336fc46ITTlD1ypVeQPSOVVYqWlyshUcdJVddnVa/aD1Jh0Qze8PMTjSzlgiWj0gKS+omaaikx8ysXx3rLpJ0iqR9JO0t6SRJv2uB/oAtxvLly3XIIYeoa9euuuWWW5pUa9mCBbri2GP147ffyjmnVUuW6M8XXqgvP/ggrXrOOY0ZOlRVpaWKRiLe6+Hycn392mua+9FHKddc9MYbqli2TK5GvQ2iFRWa98wzCq1alVLNottvlysvr/e4Ky9X0e23p9wrtg4tPB8lZiTQbMaMGaPu3burX79+mjVrVpNqPXTttXrlkUcUKitTtLpaX/7nP/rdYYelvZXzh4kTNf3f/1a4xvyJRiKqKi3VmN/+Nq26U6+5RtGKijqPRSsrNSPFWRaaPFnhBQukaLTuBc4pVl6u0rfeSrFTtLZUBlq5pJckLTGzv5jZLpujITPLlTRE0s3OuTLn3KeS3pR0Th3Lz5V0r3NuiXNuqaR7JZ23OfoCtlQXX3yxpkyZoqKiIt133336KI3gtcFbzzyj6lrhq7KiQs+ludVy1Q8/qHjJkjqPhcvLNfmZZ1Ku+eNzz6m6rKze4+b3a8k77yRdL7punarmzGl0XdWcOYquW5d0XWxVWmQ+SsxIoDktWrRIl156qVasWKHZs2dryJAhadeKRqN6/YknVFXjalq0ulprli/XzMmT06r5+TPPKFxPoFu3ZIlWzZ2bUr3ypUtVNn9+vcddNKpFb7yRUs3St9+O77JpQKy0lN02W6CkQ6Jzbqik7pJul/QrSd+b2SQzG2ZmgWbsaVdJ1c65mv/lz5BU11nSfoljja2TmV1kZoVmVljETbT4GVm2bJmqE9s8zEyrUryKVtO61atVHQ7X+Xo6qsrK5M+o/9boiuLilGtGGrjiJ8WHYLTWlpgG11dVyZK4h9H8frmqqqTrYuvRgvNRYkYCzWbNmjXy+f73q3BT/tuPRaOK1DEDzOdTSRqzTJJC69ZtfItDDb6MDFU1cEK0LtFQqNF5Fqtjxje4vsZ9+g2pvRUVbV9KW2OccyXOuceccwMk7SVpmqTHJS03s8fNbPdm6ClPUkmt19ZLyq9n7fpa6/LquufCOfeEc67AOVfQpUuXZmgT2DLcdtttCgaDys/PV/fu3XXCCSekXeuI005TIDd3o9eyAwEdc9ZZadXrvscecrFYnceycnO156BBKdfc9rDD5M/JqX+Bz6fO/fsnXc/fubOsoXoJlpMjf6dOSdfF1qWF5qPEjASazd57763+/fsrLy9PgUBAt956a9q1MrOytOeBB8p8G/9qHa2u1n6HHppWzT0HDVJWrZm7gYvF1L1fned86pXbs2ejIbHDnnumVDOw337y5eU1uMYCAQUGDEipLlpfWvdPmFkPSYMlnSipWtKrknaQ9I2Z/bGJPZVJalfrtXaSSpNY205SmWvqc3yBrcgJJ5yg77//Xu+9956++eYb5efX9btkcvofdZROHD5c2Tk5CubnKyc3V3seeKDOTONhMJKUmZOj42++WVnB4Eav+/x+Bdq314Bhw1Ku2fd3v9tkSG9gfr/yd9oppZBofr86/n979x5j6V2fB/z5etde3y/AZkVpDXEF5RJhkJf8kQRh1aoorRyiAFLNpUAgDiAHRKIoSNhgLmoKaqJGJSGC2jFGhMZVCKQpRMIJJHVIUxbBJlpEHQSxgQWy3LxeY4xZf/vHzP4yXWZm5/qeM/bnIx1pzsxvzvvsb8+Z7z5z3nP2Fa9I7dmz8po9exbWrPKsKA8N2zwfEzMStsyuXbty66235tZbb83Bgwfz6g3OshOuv/nmPHzfvpxz3nk5+7zzsuess/Km974352xw7j7thS/MWRde+EPvyH3G2WfnX7/+9Tl9Db/AXGrXGWfk8ddck11nLX+Cw+5zzsmTX//6dd3m+c973qkXPfBALnr5y9d1u8xerXVWVNXpWRh8P5fkXyX5dJJ3J3l/dx9bXPPTSW7u7gs3HGjh9RbfTvKk7v67xc/dnORwd7/upLWfSPK73f3uxes/l+Tq7l71/Xv379/fBw4c2GhEeMj70uc/n89+8pO5+HGPyxMuu2xTt9Xd+fN3vCMfftOb8v3vfjcPHD+ef3HFFXnBu9+dCx/1qA3d5pc/8pF87LnPTR8/ngcWT//Zfc45Of2CC/JvP/GJnLvOtw4/fvRovnDZZfn+nXcmJ5+Kc8YZOePii3PJpz6VXeef/G935kFVfaq792/j7U8yHxdvx4yEOfaD++/PJ//sz/Ldu+/O0664IudfdNGmbu87hw/nfS9/ef7vn/5pTtu1K2ecfXae9YY35PJf/MUN/TdRD9x/f2698sr8w1/+5Xj9fp12Wk4788w8/lWvytM28B4Dd91yS77y0pcu+9rEOvvs7Pu1X8vDN1nA2R6rzcf1lMRvJKkkv5fk3d39N8usuTDJp7v7RzeRN1X135J0kpcneUqSDyf5ie4+dNK6VyR5TRZeA9JJPprkv3T376x2+wYgzJ8Hjh/PXV/9as48//yctQVl654vfzmfe+c789WPfjS7zjor//xFL8qPXnVVTl/h1J1TOf6d7+Sr11yTo3/wB+NZxb7vvpz/sz+bR77jHdm1yX8IsH0mKImTzcfF2zIj4SHm3qNH872jR3PBIx+5of/rd6l+4IEc/uhH87nf/u189ytfyQVPeEKe+OpXr+ssm5Pd/ZGP5GuveU3uP3x44aya48dz2kUXZd/b3pYLN/iSFLbfVpXEFyX57939va0MuLpRkgAAEwtJREFUt8KxHpbkxiz8RvabSV7X3b9XVU9P8pHuPndxXSV5WxYGZZL81yS/eqpTaQxAYKOOf/vbuffTn06y8FoM5XD+TVASJ5uPi8czI4G5092579Ch/ODw4ex6xCNy5lOfuqFnO5nOlpTEBxMDEOChY7tL4oONGQnw0LDafJzqP/4FAABgB1ASAQAAGJREAAAABiURAACAQUkEAABgUBIBAAAYlEQAAAAGJREAAIBBSQQAAGBQEgEAABiURAAAAAYlEQAAgEFJBAAAYFASAQAAGJREAAAABiURAACAQUkEAABgUBIBAAAYlEQAAAAGJREAAIBBSQQAAGBQEgEAABiURAAAAAYlEQAAgEFJBAAAYFASAQAAGJREAAAABiURAACAQUkEAABgUBIBAAAYlEQAAAAGJREAAIBBSQQAAGBQEgEAABiURAAAAAYlEQAAgEFJBAAAYFASAQAAGJREAAAABiURAACAQUkEAABgUBIBAAAYlEQAAAAGJREAAIBh7kpiVT2sqv6wqu6pqjuq6vmrrL2+qu6vqmNLLpdMmRcApmA+AjCV3bMOsIzfSvL9JPuSPCXJ/6yqg919aIX1v9/dL5wsHQDMhvkIwCTm6pnEqjonyXOSXNfdx7r7tiR/lORFs00GALNjPgIwpbkqiUkel+QH3X37ks8dTPKkVb7nyqr6VlUdqqpXbm88AJgJ8xGAycxbSTw3ydGTPndXkvNWWH9Lkick2Zvk55O8oaquWm5hVV1dVQeq6sCRI0e2Ki8ATGHb5mNiRgLw/5u0JFbVx6uqV7jcluRYkvNP+rbzk9y93O1192e7+3B3H+/uTyT5zSTPXWHtu7p7f3fv37t371b+sQBgU2Y5HxfXm5EADJO+cU13X77a1xdfc7G7qh7b3X+3+OlLk6z0ovwfOkSS2nhCAJie+QjAPJmr0027+54kH0jy5qo6p6p+Msmzk7x3ufVV9eyquqgW/HiSVyf50HSJAWD7mY8ATGmuSuKiVyU5K8k/JHl/kleeeHvvqnp6VR1bsvbfJfl8Fk63uTnJ27r7PRPnBYApmI8ATGLu/p/E7v5Wkp9Z4Wv/Kwsv3j9xfcUX4QPAg4n5CMBU5vGZRAAAAGZESQQAAGBQEgEAABiURAAAAAYlEQAAgEFJBAAAYFASAQAAGJREAAAABiURAACAQUkEAABgUBIBAAAYlEQAAAAGJREAAIBBSQQAAGBQEgEAABiURAAAAAYlEQAAgEFJBAAAYFASAQAAGJREAAAABiURAACAQUkEAABgUBIBAAAYlEQAAAAGJREAAIBBSQQAAGBQEgEAABiURAAAAAYlEQAAgEFJBAAAYFASAQAAGJREAAAABiURAACAQUkEAABgUBIBAAAYlEQAAAAGJREAAIBBSQQAAGBQEgEAABiURAAAAAYlEQAAgEFJBAAAYFASAQAAGJREAAAABiURAACAYa5KYlVdU1UHquq+qrppDetfW1Vfq6qjVXVjVe2ZICYATM6MBGAqc1USkxxO8tYkN55qYVU9M8nrklyR5NFJLknypm1NBwCzY0YCMIm5Kond/YHu/mCSb65h+YuT3NDdh7r720nekuQl25kPAGbFjARgKnNVEtfpSUkOLrl+MMm+qnr4cour6urF03QOHDlyZJKAADAjZiQAG7aTS+K5Se5acv3Ex+ctt7i739Xd+7t7/969e7c9HADMkBkJwIZNVhKr6uNV1StcbtvATR5Lcv6S6yc+vnvzaQFgOmYkAPNk91QH6u7Lt/gmDyW5NMkti9cvTfL17l7LazUAYG6YkQDMk7k63bSqdlfVmUl2JdlVVWdW1UpF9uYkL6uqJ1bVhUmuTXLTRFEBYFJmJABTmauSmIUhdm8W3rb7hYsfX5skVXVxVR2rqouTpLv/JMnbk3wsyZ1J7kjyxlmEBoAJmJEATKK6e9YZJrd///4+cODArGMAMIGq+lR37591jp3CjAR4aFhtPs7bM4kAAADMkJIIAADAoCQCAAAwKIkAAAAMSiIAAACDkggAAMCgJAIAADAoiQAAAAxKIgAAAIOSCAAAwKAkAgAAMCiJAAAADEoiAAAAg5IIAADAoCQCAAAwKIkAAAAMSiIAAACDkggAAMCgJAIAADAoiQAAAAxKIgAAAIOSCAAAwKAkAgAAMCiJAAAADEoiAAAAg5IIAADAoCQCAAAwKIkAAAAMSiIAAACDkggAAMCgJAIAADAoiQAAAAxKIgAAAIOSCAAAwKAkAgAAMCiJAAAADEoiAAAAg5IIAADAoCQCAAAwKIkAAAAMSiIAAACDkggAAMCgJAIAADAoiQAAAAxzVRKr6pqqOlBV91XVTadY+5KqOl5Vx5ZcLp8mKQBMy4wEYCq7Zx3gJIeTvDXJM5OctYb1f9XdP7W9kQBgLpiRAExirkpid38gSapqf5J/OuM4ADA3zEgApjJXp5tuwFOr6htVdXtVXVdVK5beqrp68TSdA0eOHJkyIwDMghkJwIbs5JL4F0l+LMmPJHlOkquS/MpKi7v7Xd29v7v37927d6KIADATZiQAGzZZSayqj1dVr3C5bb23191f6O4vdvcD3f23Sd6c5LlbnxwAtpcZCcA8mew1id19+XYfIklt8zEAYMuZkQDMk7k63bSqdlfVmUl2JdlVVWeu9BqKqnpWVe1b/PjxSa5L8qHp0gLAdMxIAKYyVyUxybVJ7k3yuiQvXPz42iSpqosX/5+nixfXXpHkb6rqniQfTvKBJP9h+sgAMAkzEoBJVHfPOsPk9u/f3wcOHJh1DAAmUFWf6u79s86xU5iRAA8Nq83HeXsmEQAAgBlSEgEAABiURAAAAAYlEQAAgEFJBAAAYFASAQAAGJREAAAABiURAACAQUkEAABgUBIBAAAYlEQAAAAGJREAAIBBSQQAAGBQEgEAABiURAAAAAYlEQAAgEFJBAAAYFASAQAAGJREAAAABiURAACAQUkEAABgUBIBAAAYlEQAAAAGJREAAIBBSQQAAGBQEgEAABiURAAAAAYlEQAAgEFJBAAAYFASAQAAGJREAAAABiURAACAQUkEAABgUBIBAAAYlEQAAAAGJREAAIBBSQQAAGBQEgEAABiURAAAAAYlEQAAgEFJBAAAYFASAQAAGJREAAAABiURAACAYW5KYlXtqaobquqOqrq7qj5TVc86xfe8tqq+VlVHq+rGqtozVV4AmIoZCcCU5qYkJtmd5EtJnpHkgiTXJrmlqh6z3OKqemaS1yW5Ismjk1yS5E1TBAWAiZmRAExmbkpid9/T3dd399939wPd/cdJvpjkshW+5cVJbujuQ9397SRvSfKSieICwGTMSACmNDcl8WRVtS/J45IcWmHJk5IcXHL9YJJ9VfXw7c4GALNkRgKwneayJFbV6Unel+Q93f25FZadm+SuJddPfHzeCrd5dVUdqKoDR44c2bqwADAhMxKA7TZZSayqj1dVr3C5bcm605K8N8n3k1yzyk0eS3L+kusnPr57ucXd/a7u3t/d+/fu3bvJPw0AbB0zEoB5snuqA3X35adaU1WV5IYk+5L8m+6+f5Xlh5JcmuSWxeuXJvl6d39zk1EBYFJmJADzZN5ON31nkickubK77z3F2puTvKyqnlhVF2bhnd5u2uZ8ADArZiQAk5ibklhVj07yC0mekuRrVXVs8fKCxa9fvHj94iTp7j9J8vYkH0tyZ5I7krxxNukBYPuYkQBMabLTTU+lu+9IUqt8/c4svBB/6ed+I8lvbHM0AJgpMxKAKc3NM4kAAADMnpIIAADAoCQCAAAwKIkAAAAMSiIAAACDkggAAMCgJAIAADAoiQAAAAxKIgAAAIOSCAAAwKAkAgAAMCiJAAAADEoiAAAAg5IIAADAoCQCAAAwKIkAAAAMSiIAAACDkggAAMCgJAIAADAoiQAAAAxKIgAAAEN196wzTK6qjiS5Y4tv9hFJvrHFt7kddkrOZOdklXPr7ZSscm6t7cr56O7euw23+6BkRsq5xXZKVjm31k7JmeycrNuRc8X5+JAsiduhqg509/5Z5ziVnZIz2TlZ5dx6OyWrnFtrp+Rk/XbK362cW2+nZJVza+2UnMnOyTp1TqebAgAAMCiJAAAADEri1nnXrAOs0U7JmeycrHJuvZ2SVc6ttVNysn475e9Wzq23U7LKubV2Ss5k52SdNKfXJAIAADB4JhEAAIBBSQQAAGBQEjegqvZU1Q1VdUdV3V1Vn6mqZ53ie15bVV+rqqNVdWNV7Zko6zVVdaCq7quqm06x9iVVdbyqji25XD5FzsXjrznr4vpZ7enDquoPq+qexfvA81dZe31V3X/Snl4y62y14G1V9c3Fy9uqqrYr1yZyTrp/yxx/PY+fmdwfF4+9ppxz8Bhf18/OWe4pG2dGzjbn4nrzcYPZzMc159wR83Hx+HM/I+dxPiqJG7M7yZeSPCPJBUmuTXJLVT1mucVV9cwkr0tyRZJHJ7kkyZumCJrkcJK3Jrlxjev/qrvPXXL5+PZF+yFrzjrjPf2tJN9Psi/JC5K8s6qetMr63z9pT78wB9muTvIzSS5N8uQkVyb5hW3MdbL17OGU+3eyNd0nZ3x/TNb3OJ/lY3zNPzvnYE/ZODNy65mP02UzH9dmp8zHZGfMyLmbj0riBnT3Pd19fXf/fXc/0N1/nOSLSS5b4VtenOSG7j7U3d9O8pYkL5ko6we6+4NJvjnF8TZjnVlnsqdVdU6S5yS5rruPdfdtSf4oyYu2+9inss5sL07y69395e7+SpJfz0T3yXnew5Ot4z45s8d4snMe5+v82TnTPWXjzMitZz5ujvm49XbKfEx2xuN8HuejkrgFqmpfksclObTCkiclObjk+sEk+6rq4dudbQOeWlXfqKrbq+q6qto960ArmNWePi7JD7r79pOOvdpvSq+sqm9V1aGqeuWcZFtu/1b7M2yl9e7hVPu3GR7jG3CKn507aU9ZhRk5OfNxc9nMx621kx7fyZw8xudhPiqJm1RVpyd5X5L3dPfnVlh2bpK7llw/8fF525ltA/4iyY8l+ZEs/CbrqiS/MtNEK5vVnp6b5OhJn7trlePekuQJSfYm+fkkb6iqq+Yg23L7d+5Er7tYT84p928zPMbXaQ0/O3fKnrIKM3ImzMfNZTMft9ZOeXwnc/IYn5f5qCQuo6o+XlW9wuW2JetOS/LeLJw7fs0qN3ksyflLrp/4+O4pcq5Vd3+hu7+4+DT33yZ5c5LnbibjdmXN7Pb05OOeOPayx+3uz3b34e4+3t2fSPKb2aI9XcZ6si23f8d6mv84dc05J96/zdiW++NW287H+Hqs8WfnjtjThyIzcmsfP+aj+bjKsU8c33ycwDzMyHmaj0riMrr78u6uFS4/lSy8+1WSG7LwwuLndPf9q9zkoSy8APqES5N8vbs3dW70WnJuUifZkt+cbUPWWe3p7Ul2V9VjTzr2SqdR/dAhskV7uoz1ZFtu/9b6Z9iszezhdu7fZmzL/XECk+/nOn527tQ9fdAzI//xENmCx4/5+I+HiPloPs6XSfd03uajkrhx78zC0/xXdve9p1h7c5KXVdUTq+rCLLxj0U3bnC9JUlW7q+rMJLuS7KqqM1c6v7qqnrV4DnSq6vFJrkvyoSlyrjdrZrSn3X1Pkg8keXNVnVNVP5nk2Vn4rc8PqapnV9VFteDHk7w627Sn68x2c5JfqqpHVdU/SfLLmeg+uZ6cU+7fctZxn5zZY3w9OWf9GF+01p+dM91TNs2MnFHOmI+bzWY+rsFOmY/JjpqR8zUfu9tlnZcsvN1sJ/leFp7yPXF5weLXL168fvGS7/mlJF/Pwrnmv5tkz0RZr1/MuvRy/XI5k/ynxYz3JPlCFp5mP33CfV1z1hnv6cOSfHBxn+5M8vwlX3t6Fk5LOXH9/Vl4N61jST6X5NWzyLZMrkry9iTfWry8PUlN+He91pyT7t9a75PzdH9cT845eIyv+LNz3vbUZXv+nhe/Pjd/1ys9dpbLOcvHz3pyzng/zcfpcpqPW5x1xo/xuZuPtXggAAAAcLopAAAA/0hJBAAAYFASAQAAGJREAAAABiURAACAQUkEAABgUBIBAAAYlEQAAAAGJREAAIBBSYQHsaraW1Vfrao3Lvnck6vqe1X1vFlmA4BZMR9hddXds84AbKOqemaS/5HkGUk+k+RAkv/T3S+daTAAmCHzEVamJMJDQFX95yQ/neTPkzw9yVO6+9hsUwHAbJmPsDwlER4CqmpPkoNJHpvkJ7r7r2ccCQBmznyE5XlNIjw0PCbJP0vSSS6ZbRQAmBuPifkIP8QzifAgV1WnJ/nfSW5P8tdJ3pjk0u6+c6bBAGCGzEdYmZIID3JV9R+TPD/Jk5PcleQjSc5M8i+7+4FZZgOAWTEfYWVON4UHsap6RpJfTvLvu/s7vfBboZckeWKSX51lNgCYFfMRVueZRAAAAAbPJAIAADAoiQAAAAxKIgAAAIOSCAAAwKAkAgAAMCiJAAAADEoiAAAAg5IIAADAoCQCAAAw/D9ar6G8Dzy9vAAAAABJRU5ErkJggg==\\n\"\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n }\n }\n ],\n \"source\": [\n \"# Perform Matrix Multiplication\\n\",\n \"### ENTER CODE HERE ###\\n\",\n \"X_trans = np.dot(A13, np.transpose(X))\\n\",\n \"\\n\",\n \"# Plot Transformation\\n\",\n \"### ENTER CODE HERE ###\\n\",\n \"plotTransformedData(pd.DataFrame(X, columns=['x','y']), pd.DataFrame(np.transpose(X_trans), columns=['x','y']), colors, sizes, limits)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"BKxaMG1smenY\"\n },\n \"source\": [\n \"For the rest of the following linear transformations, you can Google the matrix transformation definitions to learn more.\\n\",\n \"### Rotation Matrix\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 140,\n \"metadata\": {\n \"colab\": {\n \"base_uri\": \"https://localhost:8080/\",\n \"height\": 411\n },\n \"id\": \"7-TAR3HGmenZ\",\n \"outputId\": \"e6054ffe-4216-402a-b8b4-6896cb7e01b0\"\n },\n \"outputs\": [\n {\n \"output_type\": \"display_data\",\n \"data\": {\n \"text/plain\": [\n \"
\"\n ],\n \"image/png\": 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\\n\"\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n }\n }\n ],\n \"source\": [\n \"# Perform Matrix Multiplication\\n\",\n \"### ENTER CODE HERE ###\\n\",\n \"X_trans = np.dot(A3, np.transpose(X)) \\n\",\n \"\\n\",\n \"# Plot Transformation\\n\",\n \"### ENTER CODE HERE ###\\n\",\n \"plotTransformedData(pd.DataFrame(X, columns=['x','y']), pd.DataFrame(np.transpose(X_trans), columns=['x','y']), colors, sizes, limits)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"_K-VuIcLmena\"\n },\n \"source\": [\n \"### Reflection Matrices\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 141,\n \"metadata\": {\n \"colab\": {\n \"base_uri\": \"https://localhost:8080/\",\n \"height\": 411\n },\n \"id\": \"H6Xvk5BImenb\",\n \"outputId\": \"9362a53f-4d2d-431a-d21a-3943a81cb52c\"\n },\n \"outputs\": [\n {\n \"output_type\": \"display_data\",\n \"data\": {\n \"text/plain\": [\n \"
\"\n ],\n \"image/png\": 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\\n\"\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n }\n }\n ],\n \"source\": [\n \"# Perform Matrix Multiplication\\n\",\n \"### ENTER CODE HERE ###\\n\",\n \"X_trans = np.dot(A11, np.transpose(X)) # about X-axis\\n\",\n \"\\n\",\n \"# Plot Transformation\\n\",\n \"### ENTER CODE HERE ###\\n\",\n \"plotTransformedData(pd.DataFrame(X, columns=['x','y']), pd.DataFrame(np.transpose(X_trans), columns=['x','y']), colors, sizes, limits)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 142,\n \"metadata\": {\n \"colab\": {\n \"base_uri\": \"https://localhost:8080/\",\n \"height\": 411\n },\n \"id\": \"JvkK6qIDmenc\",\n \"outputId\": \"33f3d16c-c96b-46ed-951c-28cd39024fc3\"\n },\n \"outputs\": [\n {\n \"output_type\": \"display_data\",\n \"data\": {\n \"text/plain\": [\n \"
\"\n ],\n \"image/png\": 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\\n\"\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n }\n }\n ],\n \"source\": [\n \"# Perform Matrix Multiplication\\n\",\n \"### ENTER CODE HERE ###\\n\",\n \"X_trans = np.dot(A4, np.transpose(X)) # about y-axis\\n\",\n \"\\n\",\n \"# Plot Transformation\\n\",\n \"### ENTER CODE HERE ###\\n\",\n \"plotTransformedData(pd.DataFrame(X, columns=['x','y']), pd.DataFrame(np.transpose(X_trans), columns=['x','y']), colors, sizes, limits)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 143,\n \"metadata\": {\n \"colab\": {\n \"base_uri\": \"https://localhost:8080/\",\n \"height\": 411\n },\n \"id\": \"Qp7BgAU2mend\",\n \"outputId\": \"6683f93f-2615-407e-8b07-e066b6e8d0f6\"\n },\n \"outputs\": [\n {\n \"output_type\": \"display_data\",\n \"data\": {\n \"text/plain\": [\n \"
\"\n ],\n \"image/png\": 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\\n\"\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n }\n }\n ],\n \"source\": [\n \"# Perform Matrix Multiplication\\n\",\n \"### ENTER CODE HERE ###\\n\",\n \"X_trans = np.dot(A1, np.transpose(X)) # about origin\\n\",\n \"\\n\",\n \"# Plot Transformation\\n\",\n \"### ENTER CODE HERE ###\\n\",\n \"plotTransformedData(pd.DataFrame(X, columns=['x','y']), pd.DataFrame(np.transpose(X_trans), columns=['x','y']), colors, sizes, limits)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 144,\n \"metadata\": {\n \"colab\": {\n \"base_uri\": \"https://localhost:8080/\",\n \"height\": 411\n },\n \"id\": \"rcqyzN_cmene\",\n \"outputId\": \"35a86222-8ac3-4f4e-c366-6dabdc985eec\"\n },\n \"outputs\": [\n {\n \"output_type\": \"display_data\",\n \"data\": {\n \"text/plain\": [\n \"
\"\n ],\n \"image/png\": 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\\n\"\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n }\n }\n ],\n \"source\": [\n \"# Perform Matrix Multiplication\\n\",\n \"### ENTER CODE HERE ###\\n\",\n \"X_trans = np.dot(A12, np.transpose(X)) #about y=x\\n\",\n \"\\n\",\n \"# Plot Transformation\\n\",\n \"### ENTER CODE HERE ###\\n\",\n \"plotTransformedData(pd.DataFrame(X, columns=['x','y']), pd.DataFrame(np.transpose(X_trans), columns=['x','y']), colors, sizes, limits)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 145,\n \"metadata\": {\n \"colab\": {\n \"base_uri\": \"https://localhost:8080/\",\n \"height\": 411\n },\n \"id\": \"UXWPtQJOmeng\",\n \"outputId\": \"28bd6aa2-ebbd-4e15-bd74-49b5d50b3ea5\"\n },\n \"outputs\": [\n {\n \"output_type\": \"display_data\",\n \"data\": {\n \"text/plain\": [\n \"
\"\n ],\n \"image/png\": 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\\n\"\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n }\n }\n ],\n \"source\": [\n \"# Perform Matrix Multiplication\\n\",\n \"### ENTER CODE HERE ###\\n\",\n \"X_trans = np.dot(A8, np.transpose(X)) #about y = -x\\n\",\n \"\\n\",\n \"# Plot Transformation\\n\",\n \"### ENTER CODE HERE ###\\n\",\n \"plotTransformedData(pd.DataFrame(X, columns=['x','y']), pd.DataFrame(np.transpose(X_trans), columns=['x','y']), colors, sizes, limits)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"Ny3HHFLBmenh\"\n },\n \"source\": [\n \"### Contraction and Expansion Matrices\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 146,\n \"metadata\": {\n \"colab\": {\n \"base_uri\": \"https://localhost:8080/\",\n \"height\": 411\n },\n \"id\": \"i4b2jx1Zmeni\",\n \"outputId\": \"55ff8011-6cca-40b1-f900-b38bce3f896c\"\n },\n \"outputs\": [\n {\n \"output_type\": \"display_data\",\n \"data\": {\n \"text/plain\": [\n \"
\"\n ],\n \"image/png\": 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\\n\"\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n }\n }\n ],\n \"source\": [\n \"# Perform Matrix Multiplication\\n\",\n \"### ENTER CODE HERE ###\\n\",\n \"X_trans = np.dot(A2, np.transpose(X)) # horizontal contraction\\n\",\n \"\\n\",\n \"# Plot Transformation\\n\",\n \"### ENTER CODE HERE ###\\n\",\n \"plotTransformedData(pd.DataFrame(X, columns=['x','y']), pd.DataFrame(np.transpose(X_trans), columns=['x','y']), colors, sizes, limits)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 147,\n \"metadata\": {\n \"colab\": {\n \"base_uri\": \"https://localhost:8080/\",\n \"height\": 411\n },\n \"id\": \"YCepBgYEmenj\",\n \"outputId\": \"c856d108-1d40-476a-c63d-3d499e801f4a\"\n },\n \"outputs\": [\n {\n \"output_type\": \"display_data\",\n \"data\": {\n \"text/plain\": [\n \"
\"\n ],\n \"image/png\": 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\\n\"\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n }\n }\n ],\n \"source\": [\n \"# Perform Matrix Multiplication\\n\",\n \"### ENTER CODE HERE ###\\n\",\n \"X_trans = np.dot(A5, np.transpose(X)) # vertical expansion\\n\",\n \"\\n\",\n \"# Plot Transformation\\n\",\n \"### ENTER CODE HERE ###\\n\",\n \"plotTransformedData(pd.DataFrame(X, columns=['x','y']), pd.DataFrame(np.transpose(X_trans), columns=['x','y']), colors, sizes, limits)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"FQai-rLdmenl\"\n },\n \"source\": [\n \"### Shearing Matrices\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 148,\n \"metadata\": {\n \"colab\": {\n \"base_uri\": \"https://localhost:8080/\",\n \"height\": 411\n },\n \"id\": \"QdWAdVizmenm\",\n \"outputId\": \"1436fe9e-9033-4688-c920-95f3ede886fd\"\n },\n \"outputs\": [\n {\n \"output_type\": \"display_data\",\n \"data\": {\n \"text/plain\": [\n \"
\"\n ],\n \"image/png\": 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\\n\"\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n }\n }\n ],\n \"source\": [\n \"# Perform Matrix Multiplication\\n\",\n \"### ENTER CODE HERE ###\\n\",\n \"X_trans = np.dot(A6, np.transpose(X)) #along Y-direction\\n\",\n \"\\n\",\n \"# Plot Transformation\\n\",\n \"### ENTER CODE HERE ###\\n\",\n \"plotTransformedData(pd.DataFrame(X, columns=['x','y']), pd.DataFrame(np.transpose(X_trans), columns=['x','y']), colors, sizes, limits)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 149,\n \"metadata\": {\n \"colab\": {\n \"base_uri\": \"https://localhost:8080/\",\n \"height\": 411\n },\n \"id\": \"ijFrEOTjmenm\",\n \"outputId\": \"d6a4f627-1040-4ac3-e149-f8293d750df0\"\n },\n \"outputs\": [\n {\n \"output_type\": \"display_data\",\n \"data\": {\n \"text/plain\": [\n \"
\"\n ],\n \"image/png\": 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\\n\"\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n }\n }\n ],\n \"source\": [\n \"# Perform Matrix Multiplication\\n\",\n \"### ENTER CODE HERE ###\\n\",\n \"X_trans = np.dot(A7, np.transpose(X)) # along X-direction\\n\",\n \"\\n\",\n \"# Plot Transformation\\n\",\n \"### ENTER CODE HERE ###\\n\",\n \"plotTransformedData(pd.DataFrame(X, columns=['x','y']), pd.DataFrame(np.transpose(X_trans), columns=['x','y']), colors, sizes, limits)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"PWHmDIjhmenn\"\n },\n \"source\": [\n \"### Projection Matrices\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 150,\n \"metadata\": {\n \"colab\": {\n \"base_uri\": \"https://localhost:8080/\",\n \"height\": 411\n },\n \"id\": \"Hdz1fZkGmeno\",\n \"outputId\": \"8c894738-80b6-4fe7-ca4a-d3da03c7383b\"\n },\n \"outputs\": [\n {\n \"output_type\": \"display_data\",\n \"data\": {\n \"text/plain\": [\n \"
\"\n ],\n \"image/png\": 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\\n\"\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n }\n }\n ],\n \"source\": [\n \"# Perform Matrix Multiplication\\n\",\n \"### ENTER CODE HERE ###\\n\",\n \"X_trans = np.dot(A9, np.transpose(X)) # on X-axis\\n\",\n \"\\n\",\n \"# Plot Transformation\\n\",\n \"### ENTER CODE HERE ###\\n\",\n \"plotTransformedData(pd.DataFrame(X, columns=['x','y']), pd.DataFrame(np.transpose(X_trans), columns=['x','y']), colors, sizes, limits)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 151,\n \"metadata\": {\n \"colab\": {\n \"base_uri\": \"https://localhost:8080/\",\n \"height\": 411\n },\n \"id\": \"_4ifE54-menp\",\n \"outputId\": \"01df407e-e53c-4ba9-eea9-063a86240910\"\n },\n \"outputs\": [\n {\n \"output_type\": \"display_data\",\n \"data\": {\n \"text/plain\": [\n \"
\"\n ],\n \"image/png\": 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\\n\"\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n }\n }\n ],\n \"source\": [\n \"# Perform Matrix Multiplication\\n\",\n \"### ENTER CODE HERE ###\\n\",\n \"X_trans = np.dot(A10, np.transpose(X)) # on Y-axis\\n\",\n \"\\n\",\n \"# Plot Transformation\\n\",\n \"### ENTER CODE HERE ###\\n\",\n \"plotTransformedData(pd.DataFrame(X, columns=['x','y']), pd.DataFrame(np.transpose(X_trans), columns=['x','y']), colors, sizes, limits)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"_h_SVj3smenq\"\n },\n \"source\": [\n \"# Connect the Dots\\n\",\n \"\\n\",\n \"In this section, you must correctly label linear transformations their names. The pool of transformations is given below:\\n\",\n \"\\n\",\n \"- Identity Matrix\\n\",\n \"- Rotation Matrix\\n\",\n \"- Reflection through the x Axis Matrix\\n\",\n \"- Reflection through the y Axis Matrix\\n\",\n \"- Reflection through the Line y = x Matrix\\n\",\n \"- Reflection through the Line y = -x Matrix\\n\",\n \"- Reflection through the Origin Matrix\\n\",\n \"- Horizontal Contraction/Expansion Matrix\\n\",\n \"- Vertical Contraction/Expansion Matrix\\n\",\n \"- Hortizontal Shear Matrix\\n\",\n \"- Vertical Shear Matrix\\n\",\n \"- Projection onto x Axis Matrix\\n\",\n \"- Projection onto y Axis Matrix\\n\",\n \"\\n\",\n \"You must correctly label the following linear transformations with the above names.\\n\",\n \"\\n\",\n \"1. A1: Reflection through the Origin Matrix\\n\",\n \"2. A2: Horizontal Contraction/Expansion Matrix\\n\",\n \"3. A3: Rotation Matrix\\n\",\n \"4. A4: Reflection through the y Axis Matrix\\n\",\n \"5. A5: Vertical Contraction/Expansion Matrix\\n\",\n \"6. A6: Vertical Shear Matrix\\n\",\n \"7. A7: Hortizontal Shear Matrix\\n\",\n \"8. A8: Reflection through the Line y = -x Matrix\\n\",\n \"9. A9: Projection onto x Axis Matrix\\n\",\n \"10. A10: Projection onto y Axis Matrix\\n\",\n \"11. A11: Reflection through the x Axis Matrix\\n\",\n \"12. A12: Reflection through the Line y = x Matrix\\n\",\n \"13. A13: Identity Matrix\\n\",\n \"\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 151,\n \"metadata\": {\n \"id\": \"VPEZLAqCmens\"\n },\n \"outputs\": [],\n \"source\": []\n }\n ],\n \"metadata\": {\n \"kernelspec\": {\n \"display_name\": \"Python 3\",\n \"language\": \"python\",\n \"name\": \"python3\"\n },\n \"language_info\": {\n \"codemirror_mode\": {\n \"name\": \"ipython\",\n \"version\": 3\n },\n \"file_extension\": \".py\",\n \"mimetype\": \"text/x-python\",\n \"name\": \"python\",\n \"nbconvert_exporter\": \"python\",\n \"pygments_lexer\": \"ipython3\",\n \"version\": \"3.8.5\"\n },\n \"colab\": {\n \"provenance\": [],\n \"collapsed_sections\": []\n }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 0\n}","dateCreated":"2022-12-16T00:00:00.000Z","url":[],"upvoteCount":482,"author":{"@type":"Person","name":"Chinni Guna Venkata Prasanth","url":"https://tutorbin.com/tutor"}}}}
Question

Assignment 5: Matrix as a Linear Transformation

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