{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## CS 132 Homework 01 Solution\n", "\n", "### Due Wednesday July 14th at Midnight (1 minute after 11:59pm) in Gradescope (with grace period of 6 hours)\n", "### Homeworks may be submitted up to 24 hours late with a 10% penalty (same grace period)\n", "\n", "In this first homework, you will become familiar with how to use Jupyter Notebooks to write text and display the results of Python code. In addition, we will do some basic analytical exercises based on\n", "the lectures this week. All homeworks in the course will be written in notebooks and submitted in Gradescope. \n", "\n", "For additional help, check out the tutorials in my tutoral directory linked from the class web page. \n", "\n", "My YouTube channel contains video presentations of the Markdown Tutorial and the basic Python for CS 237/132 Tutorial. \n", "\n", "Please read through the entire notebook, reading the expository material and then do the problems, following the instuctions to try various features; among the exposition of various features of Python there\n", "are three problems which will be graded. The homework is worth 30 points. \n", "\n", "You will need to complete this notebook and then convert to a PDF file in order to submit to Gradescope. Instructions are given here:\n", "\n", "https://www.cs.bu.edu/fac/snyder/cs132/HWSubmissionInstructions.html\n", "\n" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "# Here are some imports which will be used in the code in the rest of the lab \n", "\n", "# Imports used for the code in CS 237\n", "\n", "import numpy as np # arrays and functions which operate on arrays\n", "\n", "import matplotlib.pyplot as plt # normal plotting\n", "\n", "\n", "# NOTE: You may not use any other libraries than those listed here without explicit permission." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Basic Jupyter Notebook Concepts\n", "\n", "A Jupyter notebook contains two types of cells: Code cells and Markdown cells, the first for writing and\n", "running Python code, and the second for typesetting text and mathematics. \n", "\n", "This cell is a Markdown cell, and contains text. \n", "\n", "A code cell contains Python code and will appear as follows:" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "This is a code cell!\n" ] }, { "data": { "text/plain": [ "9" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "print(\"This is a code cell!\")\n", "\n", "x = 4\n", "x + 5" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can add and delete cells, and change their type using the menu at the top of the window,\n", "and there are useful shortcuts for most commands: for example, to run a cell, hold down Control and\n", "then hit Return; to change a cell from Markdown to Code, select the cell and type \"y\" and to turn\n", "a Code cell to Markdown, select it and type \"m\". " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Markdown: Typesetting in Notebooks\n", "\n", "Markdown is the language which is used to format text in cells which are indicated to be of Markdown type. \n", "\n", "**(A)** If you simply type text, it will be formatted with line breaks according to the width of the cell (as with HTML in a web page--if you change the width of this window, you will see the effect). \n", "\n", "To get a line break, put a slash at the end of the line. \n", "\n", "So\n", "\n", " Hello\\\n", " World\n", " \n", "would be rendered as\n", "\n", "Hello\\\n", "World\n", "\n", "\n", "The same effect occurs if you put two blank spaces at the end,\n", "but the slash is better because you can see it. \n", "\n", "To separate text into paragraphs, with a blank line between, \n", "simply insert a blank line.\n", "\n", "There is a blank line above this one. \n", "\n", "This is the second paragraph, which is going to be followed by a third.\n", "\n", "Yup, here is the third. \n", "\n", "\n", "This *usually* works fine, but if in doubt, leave two blank lines!\n", "\n", "**(B)** The other thing you can do, if you don't know anything better, is to **indent** the\n", "text -- Markdown will assume that this is \"preformatted text\" as with the HTML `
` command. \n",
    "\n",
    "    Here I have simply hit a tab before the line, and\n",
    "    so it will simply give me the characters I type with no\n",
    "    attempt to format them.  So I can type  this  and\n",
    "    it will not be formatted. \n",
    "    \n",
    "**(C)**  So the simplest thing is to write text as normal, \n",
    "\n",
    "    and then indented, so you can just use \"ASCII Art\" or \"ASCII Math\" to\n",
    "    write your answers:\n",
    "    \n",
    "    The probability of getting a Head for the first time after K tosses\n",
    "    is P( 2^k ), and the probability of getting a head in the first 4 tosses\n",
    "    is hence:\n",
    "    \n",
    "             P( Heads within 4 tosses ) = 1/2 + 1/4 + 1/8 + 1/16 = 15/16. \n",
    "             \n",
    "In the next problem, we will explore how to do this with Latex, so you can get better-looking\n",
    "math:\n",
    "\n",
    "$$P(\\,\\text{Heads within $4$ tosses}\\,) = \\frac{1}{2^1} + \\frac{1}{2^2} + \\frac{1}{2^3} + \\frac{1}{2^4}  = \\frac{1}{2} + \\frac{1}{4} + \\frac{1}{8} + \\frac{1}{16}  = \\frac{15}{16}.$$\n",
    "\n",
    "\n",
    "\n",
    "**(D)**  If for any reason, you need a line break, you can use the HTML command for a break, as shown here:\n",
    "\n",
    "    This is a line with a 
break in the middle, and now,
another one. \n", "\n", "This is a line with a
break in the middle, and now,
another one. " ] }, { "attachments": { "Screen%20Shot%202021-05-24%20at%2011.27.31%20PM.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "## Problem 1\n", "\n", "Create a cell below this one by selecting this cell (click to the left of the cell), and then typing \"b\"; then\n", "convert it from a code cell (the default) to a Markdown cell, and write your favorite Haiku (Google for examples\n", "if you don't have a favorite). \n", "\n", "Here is my favorite, by an American author:\n", "\n", "![Screen%20Shot%202021-05-24%20at%2011.27.31%20PM.png](attachment:Screen%20Shot%202021-05-24%20at%2011.27.31%20PM.png)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " Arms folded\n", " To the moon\n", " Among the cows.\n", " - Jack Kerouac" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Basic Latex\n", "\n", "Latex allows you to typeset math expressions, using dollar signs `$` to indicate\n", "the beginning and ending of \"math mode.\" \n", "\n", "\n", "There are two modes in Latex, essentially inline and display math:\n", "\n", "**(A)** Inline Mode (surround a math expression with $):\n", "\n", " If you enclose a math expression in single dollar signs, it will be rendered\n", " in-line: $2^0 + 2^1 + 2^2 + 2^3$.\n", "\n", "If you enclose a math expression in single dollar signs, it will be rendered in-line: $2^0 + 2^1 + 2^2 + 2^3$.\n", "\n", "This works fine for simple mathematical statements:\n", "\n", " $P(H) = 0.5$\n", "\n", "$P(H) = 0.5$\n", "\n", " \n", "**(B)** Display Mode (surround a math expression with $$):\n", "\n", " If you enclose a math expression in double dollar signs, separated by blank lines, \n", " it will be centered in its own paragraph:\n", " \n", " $$2^0 + 2^1 + 2^2 + 2^3$$.\n", "\n", "If you enclose a math expression in double dollar signs, separated by blank lines, \n", "it will be centered in its own paragraph:\n", " \n", "$$2^0 + 2^1 + 2^2 + 2^3$$.\n", "\n", "**(C)** Making superscripts and subscripts is easy, using `^` (hat) and `_` (underscore), but make sure to put the whole sub- or superscripted\n", "expression in curly braces, that is, make sure you do this:\n", "\n", " $2^{2k+1}$\n", "\n", "$2^{2k+1}$\n", "\n", "instead of this, which is surely not correct:\n", "\n", " $2^2k+1$\n", "\n", "$2^2k+1$\n", "\n", "**(D)** \n", "\n", "The Latex `\\frac{...}{...}` command is very easy to use, as is the equivalent\n", "expression `{ ... \\over ... }`; here are some simple examples:\n", "\n", "\n", "| Expression | Latex | \n", "|----------|--------|\n", "| $\\frac{1}{2}$ | `\\frac{1}{2}` | \n", "| ${x+1 \\over y - 1}$ | `{x+1 \\over y - 1}` | \n", "| $\\frac{\\frac{x}{y} + \\frac{e^x}{\\pi}}{2z \\over 5}$ | `frac{\\frac{x}{y} + \\frac{e^x}{\\pi}}{2z \\over 5}` | \n", "\n", "**(E)** \n", "\n", "To write matrices in Latex, you can use a couple of different environments, which require\n", "using `begin` and `end` as shown here:\n", "\n", "`matrix` just presents the matrix without brackets:\n", "\n", " $\\begin{matrix}\n", " 1 & 2 & 3 \\\\\n", " 4 & 5 & 6\n", " \\end{matrix}$\n", "\n", "$\\begin{matrix}\n", "1 & 2 & 3 \\\\\n", "4 & 5 & 6\n", "\\end{matrix}$\n", "\n", "`pmatrix` adds \"parenthesis brackets\":\n", "\n", " $\\begin{pmatrix}\n", " 1 & 2 & 3 & 4\n", " \\end{pmatrix}$\n", "\n", "$\\begin{pmatrix}\n", "1 & 2 & 3 & 4\n", "\\end{pmatrix}$\n", "\n", "Of course, you can simply write a tuple with comma very simply:\n", "\n", " $(1,2,3,4)$\n", "\n", "$(1,2,3,4)$\n", "\n", "`bmatrix` adds square brackets, which are standard in linear algebra texts:\n", "\n", " $\\begin{bmatrix}\n", " 1 & 2 & 3 \\\\\n", " 4 & 5 & 6\n", " \\end{bmatrix}$\n", "\n", "$\\begin{bmatrix}\n", "1 & 2 & 3 \\\\\n", "4 & 5 & 6\n", "\\end{bmatrix}$\n", "\n", "\n", "## Basic Latex\n", "\n", "Latex allows you to typeset math expressions, using dollar signs `$` to indicate\n", "the beginning and ending of \"math mode.\" \n", "\n", "\n", "There are two modes in Latex, essentially inline and display math:\n", "\n", "**(A)** Inline Mode (surround a math expression with $):\n", "\n", " If you enclose a math expression in single dollar signs, it will be rendered\n", " in-line: $2^0 + 2^1 + 2^2 + 2^3$.\n", "\n", "If you enclose a math expression in single dollar signs, it will be rendered in-line: $2^0 + 2^1 + 2^2 + 2^3$.\n", "\n", "This works fine for simple mathematical statements:\n", "\n", " $P(H) = 0.5$\n", "\n", "$P(H) = 0.5$\n", "\n", " \n", "**(B)** Display Mode (surround a math expression with $$):\n", "\n", " If you enclose a math expression in double dollar signs, separated by blank lines, \n", " it will be centered in its own paragraph:\n", " \n", " $$2^0 + 2^1 + 2^2 + 2^3$$.\n", "\n", "If you enclose a math expression in double dollar signs, separated by blank lines, \n", "it will be centered in its own paragraph:\n", " \n", "$$2^0 + 2^1 + 2^2 + 2^3$$.\n", "\n", "**(C)** Making superscripts and subscripts is easy, using `^` (hat) and `_` (underscore), but make sure to put the whole sub- or superscripted\n", "expression in curly braces, that is, make sure you do this:\n", "\n", " $2^{2k+1}$\n", "\n", "$2^{2k+1}$\n", "\n", "instead of this, which is surely not correct:\n", "\n", " $2^2k+1$\n", "\n", "$2^2k+1$\n", "\n", "**(D)** \n", "\n", "The Latex `\\frac{...}{...}` command is very easy to use, as is the equivalent\n", "expression `{ ... \\over ... }`; here are some simple examples:\n", "\n", "\n", "| Expression | Latex | \n", "|----------|--------|\n", "| $\\frac{1}{2}$ | `\\frac{1}{2}` | \n", "| ${x+1 \\over y - 1}$ | `{x+1 \\over y - 1}` | \n", "| $\\frac{\\frac{x}{y} + \\frac{e^x}{\\pi}}{2z \\over 5}$ | `frac{\\frac{x}{y} + \\frac{e^x}{\\pi}}{2z \\over 5}` | \n", "\n", "**(E)** \n", "\n", "To write matrices in Latex, you can use a couple of different environments, which require\n", "using `begin` and `end` as shown here:\n", "\n", "`matrix` just presents the matrix without brackets:\n", "\n", " $\\begin{matrix}\n", " 1 & 2 & 3 \\\\\n", " 4 & 5 & 6\n", " \\end{matrix}$\n", "\n", "$\\begin{matrix}\n", "1 & 2 & 3 \\\\\n", "4 & 5 & 6\n", "\\end{matrix}$\n", "\n", "`pmatrix` adds \"parenthesis brackets\":\n", "\n", " $\\begin{pmatrix}\n", " 1 & 2 & 3 & 4\n", " \\end{pmatrix}$\n", "\n", "$\\begin{pmatrix}\n", "1 & 2 & 3 & 4\n", "\\end{pmatrix}$\n", "\n", "Of course, you can simply write a tuple with comma very simply:\n", "\n", " $(1,2,3,4)$\n", "\n", "$(1,2,3,4)$\n", "\n", "`bmatrix` adds square brackets, which are standard in linear algebra texts:\n", "\n", " $\\begin{bmatrix}\n", " 1 & 2 & 3 \\\\\n", " 4 & 5 & 6\n", " \\end{bmatrix}$\n", "\n", "$\\begin{bmatrix}\n", "1 & 2 & 3 \\\\\n", "4 & 5 & 6\n", "\\end{bmatrix}$\n", "\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Problem 2 \n", "\n", "Consider the following system of linear equations:\n", "$$\\begin{aligned}\n", " 2 x_1 + 4x_2 &= 4 \\\\ \n", " 5 x_1 + 7x_2 &= 14 \\\\ \n", " \\end{aligned}$$\n", "\n", "### Part A\n", "\n", "In the following cell, give the augmented matrix corresponding to this system (Hint: just cut and paste\n", "and modify from the previous cell). Give the numbers in floating-point form. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\\begin{bmatrix}\n", " 2.0 & 4.0 & 4.0 \\\\\n", " 5.0 & 7.0 & 14.0\n", "\\end{bmatrix}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Part B\n", "\n", "Solve this system using elementary row operations on the augmented matrix and give the solution\n", "as a tuple of two floating-point numbers, using Latex. Round to 4 decimal places.\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$(x_1,x_2) = (-0.6667,1.3333)$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Numpy Arrays\n", "\n", "Numpy provides an (multi-dimensional) array type, ndarray, which is exactly what we\n", "need for linear algebra computations. \n", "\n", "\n", "### Basic One-Dimensional Arrays\n", "\n", "The numpy library functions return arrays instead of normal Python lists. Since\n", "numpy automatically converts normal lists into numpy arrays, we can use lists\n", "without any problems. \n", "\n", "However, the reverse is not true: normal Python functions which expect lists will NOT\n", "work with numpy arrays, and you'll have to make adjustments. " ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[12 3 5]\n" ] } ], "source": [ "# Creating a numpy array from a list\n", "\n", "ex1 = np.array( [ 12,3,5 ] )\n", "print(ex1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Multidimensional Ndarrays\n", "\n", "Numpy is designed to provide high-speed access to multi-dimensional\n", "arrays, for linear algebra and data science. These will be used extensively in CS 132. " ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 1 2 3 4]\n", " [ 5 6 7 8]\n", " [ 9 10 11 12]]\n" ] }, { "data": { "text/plain": [ "array([[ 1, 2, 3, 4],\n", " [ 5, 6, 7, 8],\n", " [ 9, 10, 11, 12]])" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# 2D array\n", "\n", "X = np.array([[ 1, 2, 3, 4],\n", " [ 5, 6, 7, 8],\n", " [ 9, 10, 11, 12]] )\n", "\n", "print(X)\n", "X" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The size of the array along each dimension can be found using the `shape` function:" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(3, 4)" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# X has 3 rows and 4 columns\n", "np.shape(X)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Numpy array types. \n", "\n", "Numpy assigns a type to each matrix – for example, float or int. If you construct a matrix\n", "using the constructor `array`, and all of the entries are integers, then numpy will auto-detect this as an integer matrix. If even one of the values is float, then the whole matrix will be float. " ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[1, 2, 3],\n", " [5, 6, 7]])" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.array( [ [ 1, 2, 3], [5, 6, 7]])" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[1., 2., 3.],\n", " [5., 6., 7.]])" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.array( [ [ 1, 2, 3], [5, 6, 7.0]])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "When you assign values to an integer matrix they will be rounded to the nearest integer. This is not what you\n", "want. So you do not want to work with integer matrices in general.\n", "\n", "So it is a good idea to make sure that the inputs your your functions are floating point matrices. To convert an\n", "integer matrix to a floating point matrix you can convert it using the function `astype`:" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[ 1., 2., 3., 4.],\n", " [ 5., 6., 7., 8.],\n", " [ 9., 10., 11., 12.]])" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X1 = X.astype(float)\n", "X1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Problem 3\n", "\n", "### Part A\n", "\n", "Create a variable Y which holds the matrix from the previous problem:\n", "\n", "$$\\begin{bmatrix}\n", " 2.0 & 4.0 & 4.0 \\\\\n", " 5.0 & 7.0 & 14.0\n", "\\end{bmatrix}$$\n", "\n", "Be sure to create an array of floats, not integers!\n", "Simply print out the value of Y as your answer. " ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 2. 4. 4.]\n", " [ 5. 7. 14.]]\n" ] } ], "source": [ "Y = np.array( [ [2.0,4,4], [5,7,14]])\n", "print(Y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Part B\n", "\n", "Now calculate and print out an array Y1 in which you have multiplied the first row of Y by 2, and added\n", "it to the second row:\n", "\n", "$$\\begin{bmatrix}\n", " 2.0 & 4.0 & 4.0 \\\\\n", " 9.0 & 15.0 & 22.0\n", "\\end{bmatrix}$$\n", "\n", "You must calculate Y1 from Y, and not simply use `np.array`. Hint: Use `np.copy(...)` to make a fresh copy of\n", "the array Y, then make the changes to the new copy Y1. \n", "\n", "Hint: You can do this by changing each individual entry, but numpy allows you to apply arithmetic operations to\n", "entire rows, which can simplify the computation. In fact, after making the copy, you only need one line!" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 2. 4. 4.]\n", " [ 9. 15. 22.]]\n" ] } ], "source": [ "Y1 = np.copy(Y)\n", "Y1[1] = 2*Y1[0] + Y1[1]\n", "print(Y1)" ] }, { "attachments": { "Screen%20Shot%202021-07-08%20at%2010.51.22%20AM.png": { "image/png": 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" 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g+PT0NJ49e4a//vWv+MEPfoA9e/agra0NFy9exKlTp7B//34rNIV1JAESIAESCFECFLoQ7RhWy14EdNhVo3O/+tWv8NFHH6GiogL37t1DbGwsdu/ejfz8fHs1mK0hARIgARIIKAEKXUBx82bhTGBwcBC/+MUv8PHHH5t5c7dv38bhw4eRk5OD+Pj4cEbDtpMACZAACXhJgELnJUBeTgJbJeB0Oo3QnTt3DiUlJWZBxOnTp5GUlLTVIngeCZAACZAACaxJgEK3Jha+SQK+JzA8PIxf/vKXKC0txYEDB1BeXo7c3FxER0f7/mYskQRIgARIIKwIUOjCqrvZ2GASGBkZwa9//WukpaWZVa26slXn0EVERASzWrw3CZAACZCADQhQ6GzQiWyCNQiMjo7it7/9rYnQqcxVVVVZo+KsJQmQAAmQQMgToNCFfBexglYnsLKyAk1dosmF//SnP+Ho0aOora3lQgirdyzrTwIkQAIhRIBCF0KdwarYk4CKnKYt0aHVq1evmsiczqPjUKs9+5utIgESIIFgEKDQBYM67xk2BDQy99lnn6G/v98sgtDVrboQgitbw+YRYENJgARIICAEKHQBwcybhCsBFbovvvjC7OOqq1p1dWtCQkK44mC7SYAESIAE/ESAQucnsCyWBEiABEiABEiABAJFgEIXKNK8DwmQAAmQAAmQAAn4iQCFzk9gWSwJkAAJkAAJkAAJBIoAhS5QpHkfEiABEiABEiABEvATAQqdn8CyWBIgARIgARIgARIIFAEKXaBI8z4kQAIkQAIkQAIk4CcCFDo/gWWxJEACJEACJEACJBAoAhS6QJHmfUjgOwJOp9O8ys7OJhMSIAESIAES8AkBCp1PMLIQEtg6gStXrpiTDx8+vPWLeCYJkAAJkAAJbECAQrcBHH5EAv4gQKHzB1WWSQIkQALhTYBCF979z9YHgQCFLgjQeUsSIAESsDkBCp3NO5jNCz0CFLrQ6xPWiARIgASsToBCZ/UeZP0tR6C5uRkulwsNDQ2IiYlBRESE5drACpMACZAACYQWAQpdaPUHaxMGBBobGzE2Noa6ujpUVFQgNjY2DFrNJpIACZAACfiTAIXOn3RZNgmsQaCpqQkLCwuor6+Hw+FAZGTkGmfxLRIgARIgARLYOgEK3dZZ8UwS8AkBzqHzCUYWQgIkQAIk4EGAQucBgy9JIBAEKHSBoMx7kAAJkEB4EaDQhVd/s7UhQIBCFwKdwCqQAAmQgM0IUOhs1qFsTugToNCFfh+xhiRAAiRgNQJ+E7rFxWXMzi5JWoYoxMVFIzqaE7+t9nCwvv4hQKHzD1eWSgIkQALhTMBvQjc2NovennEjdOkZiUhNTUB8fHQ4s2bbScAQoNDxQSABEiABEvA1Ab8J3cjIDJ48HkLLo0EjdbveyMHBQyWSooFJVH3diSzPWgQodNbqL9aWBEiABKxAwG9Ct7CwjInxOQyL2A0MTMp/U5ieWcTu6lxUVeUiKyvJCnxYRxLwOQEKnc+RskASIAESCHsCfhM6N9nV1VX09U7g0aMhPH4yhKSkWGTnJKOoMA0lxWlIdSQwaueGxa9hQYBCFxbdzEaSAAmQQEAJ+F3oPFszPb2Azz57hHv3+pGSEofjx3agrDxD5tfFy/ZH0RQ7T1h8bVsCFDrbdi0bRgIkQAJBIxBQoVtZWZWVr4twOmV+nUTr7ovYrUgE79hb5dhbky+SFx80ELwxCQSKAIUuUKR5HxIgARIIHwIBFTo3Vk1pMjo6hx5ZBdvVNYahoSlZARuDql05OFBbaF67z+VXErAbAQqd3XqU7SEBEiCB4BMIitC5m7205EKvzK+7fbsXg4NTSEiIRnZ2isytS0dBQSo03QkPErAbgaamJiwsLKC+vh4Oh0OmGjBHo936mO0hARIggUATCKrQeTa2u2scX11+hosXn6JaVsLWS4qTXVU5ZhGFJidmuhNPWnxtZQKNjY0YGxtDXV0dKioqZP5orJWbw7qTAAmQAAmEAIGQEbrl5RUzv25ycgHfXOvE45Yh6Jy7c+eqsaMiyyycCAFerAIJeE2gubkZLpcLDQ0NkqMxBhERzM3oNVQWQAIkQAJhTiBkhM7dDy6XpDnpm0C3zK3r65/AxMQ8kpPjUClSpwsnYmOj+AvQDYtfLUmAc+gs2W2sNAmQAAmENIGQEzo3rbm5JbNY4s6dPuiuEzHRUcjJ0/l1aSiUHHaa9oQHCViRAIXOir3GOpMACZBAaBMIWaHzxNba6sTly+24dr0b+/fl45DMrysry0RiYgwjdp6g+NoSBCh0lugmVpIESIAELEXAEkKnq2E1Yjc6Oovm5nY8fDCItPQEnD79hllAERcXbSnorGx4E6DQhXf/s/UkQAIk4A8ClhA6d8NV7DR3XXf3OPr7JzEue8UmJ8eipqYA5eWZHIZ1g+LXkCZAoQvp7mHlSIAESMCSBCwldG7CCwvL6Oocw+07vRgZnkGKbB2Wn5+KYplfV1qaYYZh3efyKwmEGgEKXaj1COtDAiRAAtYnYEmhc2PXiF17+wg+/18r+gcmRebSceLtncjMSkRigsyv41CsGxW/hhABCl0IdQarQgIkQAI2IWBpoZNtYLG87JL8dUsmzcmNmz348sunqJXtw06cqDBDsTbpJzbDRgQodDbqTDaFBEiABEKEgKWFzpPhzMwiBmReXafkr9NtxHS/WIcjXhZN5EmaE4fJZed5Pl+TQLAIUOiCRZ73JQESIAH7ErCN0Hl20YMHA2hrc8r2SrOS2iQWubnfzq9TsWNiYk9SfB0MAhS6YFDnPUmABEjA3gRsKXTaZZrmpFdWxH56vgVTU/NmsURDQymys5Of7w9r765l60KVAIUuVHuG9SIBEiAB6xKwrdCtygQ73R9Wh2Lbn43gxs1u3Ls/gAP7C3DyRCXKd2Rat9dYc0sToNBZuvtYeRIgARIISQK2FTpP2pOT8xiQVbBdXeNmft342BwyMhPx5puFkr8ui2lOPGHxtd8JUOj8jpg3IAESIIGwIxAWQufuVc1f91Dm192912+GYXNyklFQ4EBJSboZik2QVCc8SMDfBJqamrCwsID6+npZuONAZGSkv2/J8kmABEiABGxOIKyEzt2Xmr/uUcsQmppaMeScxn4Zhq3ZWyByl4rEpFhERfEXrJsVv/qeQGNjoyzYGUNdXR0qKiokQhzr+5uwRBIgARIggbAiEJZCp/nrliStyeTUAnq6x9D8dQeGZceJsrIMnDmzGxkZCZS6sPpnENjGNjc3w+VyoaGhATExMYiIiAhsBXg3EiABEiAB2xEIS6Fz9+LKyqosmlCpm0BP77jJYzfknJGoSaZE7PJRUZnlPpVfScBnBDiHzmcoWRAJkAAJkMB3BMJa6DyfAs1Z19bqxLXr3YiOjjRz6ooK01AguesyZQFFfDzn13ny4uvXJ0Che312vJIESIAESGBtAhS6NbhcudKBGyJ2Or/u4MFiVFXlIj8vFQmJMRyKXYMX39oeAQrd9njxbBIgARIggc0JUOjWYDQ/vwRNddLXNyELJ9pMLrvKndl452SlROuSKHVrMONbWydAods6K55JAiRAAiSwNQIUunU4uVwrmJ1dQmfHKHr6JH/dwBSmpxclb10GDhwoNOlO1rmUb5PAhgQodBvi4YckQAIkQAKvQYBCtwVougL2yeMh3H84gEhZkJiRkYSC/FSTvy4nN8XMudtCMTyFBAwBCh0fBBIgARIgAV8ToNBtg6juD/vN1U78979PsLS0gmPHy2W3iSKkpSVILrFoit02WFrp1KWlJZMIWL9GR0cjISHBfHW3YXFxUZ6HJeh2cysrKyYViaYj0XPXOih0a1HheyRAAiRAAt4QoNBtg57+wp6fX8as7A/bKitiv7nWibm55W8TE9cUoFBWxPKwH4G2tjbcuXMHT548kSH3chw5cgSlpaXPG/rw4UN0dHTIkPy0PA9z5rOdO3fK81D4/BzPFxQ6Txp8TQIkQAIk4AsCFLrXpDg+Pid7w45JQuJp9PZOSITGhTwZhj10sMRE7GJiol6zZF4WagQmJiZw//59XL161WzVdeLECVRWVpponEqc7vwwPz+Po0ePyrzLWdy8eVOG5TPw4YcfrrmtF4Uu1HqY9SEBEiAB6xOg0HnRh5qYWFfD3r3Ti3ZZPKF7xWbnpKBIInXFxenIy0vxonReGkoEWltb8eWXX5pdHY4fPw6NwOlQ67Nnz4zQpaen46c//al573e/+53ZCeJnP/sZUlNTX5E6Cl0o9SzrQgIkQAL2IECh81E/aqTu7t1+nD/fgqysJNTWFsp/RUiSvWHj4qKZ6sRHnINVjArdpUuXzO3dQqfRuIsXL5roXVlZGT7++GPz+W9+8xuzV6t+v2PHjlf2aqXQBasXeV8SIAESsC8BCp2P+lbTnCwsuGTIbVHErs8kJu7uGcf77++WNCdFZucJH92KxQSBwFpCp8Otn376qeQr7DMRu3Pnzpma/fGPf8Tg4CBOnz6Nmpoa2WUk/oUaU+hewMFvSIAESIAEfECAQucDiC8X4RyaRo/IXG/fpEySXzCilyvpTfbtKzDRu6ioyJcv4fchTmAtoZuamjLDrSpvOgR79uxZ04o///nPGBgYwDvvvCMLZva/InQXLlyAXltbW2vOz87ORnJycogTYPVIgARIgARCmQCFzk+9o/PrZmQ17IMH/WhrGzarY3NykmV+XZqsgkxHekaizK2SpHY8LEFgLaHTCJ3KWXt7OyoqKswiCG3MH/7wBzidTpw5cwa7d++WIfe4F9pIoXsBB78hARIgARLwAQEKnQ8gblaEc2gKN2/14KuvOpCaEof6+lLsqsqRCfNxktMsxky036wMfh5cAmsJnaYo0eHT69evo6ioCD/5yU/MyledQzc5OYlPPvlEFscUm7x0nrXnkKsnDb4mARIgARLwBQEKnS8oblLGt/PrljE+Nof7ErG7/FU7VuWa48d34K23ypGYGLtJCfw42ATWErrl5WX09/fj73//uxky1VWtKnm///3vzcrWn//852ZBRETEi5FYCl2we5P3JwESIAH7EaDQBbBPVeyGndPo6h6XifQTGB2dlV/4UdhRnonyHVlMcxLAvtjOrXT4VBMLX7582Vz21ltvmblxWVlZJv9cU1OT5CMcNgmFdeXr2NiYSSqsq2FfljktgEK3Hfo8lwRIgARIYCsEKHRboeSHcwYGJiXdRb9EeCbNXLr09EQUFDhQVpYh0Z44biPmB+avW6QKneab0x0jVNB0vpymI9HFDHp0dnZiaGjIyJ3mptP3Cwp0AUzWmrek0K2JhW+SAAmQAAl4QYBC5wU8by/VhRNTUwtoutiKhw8GjNideLsSJbpoQgRP59fxsB8BCp39+pQtIgESIIFgE6DQBbkHVOrm5pYkb9kUHj8ekkS1TyWyk4gGWThx/O2KINeOt/cHAQqdP6iyTBIgARIIbwIUuhDpf902bEzm1HV0jskw7IQM4U2brcQON5Ri5xvZJmIXIlVlNbwkQKHzEiAvJwESIAESeIUAhe4VJMF/o0P2hb0n8+uePHaipMQhMpeEPElMXFScJqlO4pm/Lvhd5FUNKHRe4ePFJEACJEACaxCg0K0BJVTe0sTEF79sw+1bvWY+3dEjZWY1rEOkLjYuas0VlKFSd9ZjfQIUuvXZ8BMSIAESIIHXI0Chez1uAbnKPb9OV8RqxO7mjW5JTByPkycrsWdvPhdNBKQXfH8TCp3vmbJEEiABEgh3AhQ6CzwB8/PLkudM8tfp/DqRO51fl5AYg+qqXMmHVih7hUZboBWsopsAhc5Ngl9JgARIgAR8RYBC5yuSAShnacmFbklKfOt2L4ZkVWyKbCOmSYlzZX5dZlYS0tISAlAL3sJbAhQ6bwnyehIgARIggZcJUOheJmKR7zslWnflSgc6ZQFFfkEqdu3Kwc6d2UhKipWkxFFcOBHC/UihC+HOYdVIgARIwKIEKHQW7bjl5RXMzi5ienoBzc0dsiJ2SDaBj8R7Z6pRLlE73W2CR2gSoNCFZr+wViRAAiRgZQIUOgv33uoqoPvD9vZOoLtrDL2Sv25Y5tdlZSWjqioHe2vyERUVaeEW2rPqFy5ckB1CpnDo0CHk5+dLRJVzIO3Z02wVCZAACQSOAIUucKz9eieN1vX1TeD69W7MTC8iXrYN07l15bI3bF5+qhmK9WsFWPiWCVDotoyKJ5IACZAACWyRAIVui6CsdFpLyyAuXXqKGzd6cOzYDtQeKDRJiRNlZWxMDPPXBbsvOeQa7B7g/UmABEjAfgQodPbrUywuusz+sLqV2NVvOtDSMoSM9EScOrXTbCMWG8shvmB2O4UumPR5bxIgARKwJwEKnT371bRK05zo/DpdEdsn8+smxufgkNQm+2oKzFBsoqyI5RF4AhS6wDPnHUmABEjA7gQodHbvYWnf3NwSOtpHcOdeH8bHROocCcjPS0Wx7A1bUppuhmHDAEPINJFCFzJdwYqQAAmQgG0IUOhs05WbN0SHYp+2OfHfz1vhlNWwlZVZeOednSYhcVxcNGJjozYvhGd4TYBC5zVCFkACJEACJPASAQrdS0Ds/K2mOdFhWF0R2yVpTu7e7ZOdJ8ZQVpYpW4gVYPfuPDs3P2TaRqELma5gRUiABEjANgQodLbpyu01RBMS6/Zho7JwolPkbkyGYhMk1cmhg8UoLEpjmpPt4dzW2RS6beHiySRAAiRAAlsgQKHbAiQ7n7IqYbv79wdkJewghoamkC17wuYXOFBSnI6CQsd3aU7sTCDwbaPQBZ4570gCJEACdidAobN7D2+xfTMzi2a3icZPH2J+fhk7dmSioaEUWZlJ0NWw0dHccWKLKDc9jUK3KSKeQAIkQAIksE0CFLptArPr6SsrqzD7w4rYtcnCiRs3uvFAonZHj5TjraPlKC5Js2vTA94uCl3AkfOGJEACJGB7AhQ623fx9hs4MTGH/v5J9PRMYHx8FqMjs0iTxMS1tYWygCKDaU62j/SFKyh0L+DgNyRAAiRAAj4gQKHzAUS7FrGwsIxHEqW7K/nrJqcWkJOdbPLXae66bHmtiyh4bJ8AhW77zHgFCZAACZDAxgQodBvz4adCQMWu5eEgvmhqw8jItInU1chuE/n5DiQlxiIyKoKctkGgubkZLpdL5ig2SLQzBhER5LcNfDyVBEiABEhgDQIUujWg8K0XCehKWE1KPDk5L9uIjeLrrzswNjpnEhOfOVNtthOLjKSUvEht/e8aGxslTcwY6urqUFFRIQmduQXb+rT4CQmQAAmQwFYIUOi2QonnGAK6cELz13V3j8seseMYds4A4nE5OSlmVayujOWxOYGmpiaJei6gvr5etmFzIDKSK4g3p8YzSIAESIAENiJAoduIDj9bl8CYJCR++mzEROx0r9jExBjk5aaaRRMZmYmIj+f8uvXgcQ7demT4PgmQAAmQwOsSoNC9Ljle95xAc3M7rlzpQF/vJE6crEB1dR7y8lLMoomoKEafnoP67gWF7mUi/J4ESIAESMBbAhQ6bwnyeklEvCTpTebMUOzFi0/NIopdu7Jx8kQl0jMSQal78SGh0L3Ig9+RAAmQAAl4T4BC5z1DliAEXK4V6G4THR2j6O2bwODAlPm+ujoHe/fkIyc3hZy+I0Ch46NAAiRAAiTgawIUOl8TZXlwDk3j8eMhPHw0iGTZNiwlJV4WTiSjpOTb/HXhvo0YhY7/SEiABEiABHxNgELna6Is7zkBHYq9eaMH/3fhMZaWXDh2rBz7agpl14kExMdFIypM94el0D1/RPiCBEiABEjARwQodD4CyWJeJaD56zQp8fTUIh4/GcLVqx0YHp7F0aNlOFhXjLz81FcvCoN3KHRh0MlsIgmQAAkEmACFLsDAw/F24nVmT9hOmV/XLfvDDg1Nmd0RiorTcOhgMVJT48Nq4QSFLhz/FbDNJEACJOBfAhQ6//Jl6R4EdOHE2Ngs7t7tR2fXGFZXVlBeloms7CTkSnLicFk4QaHzeCj4kgRIgARIwCcEKHQ+wchCtktAo3T37/fjzp0+SUIcjZ07s3HgQJFJUByn8+tsnL+OQrfdp4XnkwAJkAAJbEaAQrcZIX7uFwIardP9YXWO3Y3rXbguiyeGBqdx5mwV9u8vRHZ2sl/uGwqFUuhCoRdYBxIgARKwFwEKnb3605KtGRycQo/sD9vTOwGncwrR0VEolRQn+/YXIC0twXbROgqdJR9TVpoESIAEQpoAhS6kuyd8Kre8vIKJiTlcv96NXhE7YNXMqSsrzUBxURpSHQmykMIePJqamiQyuYD6+no4HA5ERnJ7NHv0LFtBAiRAAsEjQKELHnveeR0CfbLTxI0b3bI/bCeKZSXsm7VFKN+RieTkODPfLsLiZtfY2CiLQ8ZQV1eHiooKxMbGrkOCb5MACZAACZDA1ghQ6LbGiWcFkIBG63Rune4P29IyAN0fNkL+9+67lWg4XIaEhJgA1sb3t2pubpat0lxoaGhATEyMSeHi+7uwRBIgARIggXAiQKELp962WFt14cSwcxqdneOyP+w4RkZmzZ6xu6vzsKsqW7YTs+b+sJxDZ7EHkdUlARIgAQsQoNBZoJNYRaC/bxK37/Ti6dNhJMn+sHl5KSgsTENZWYb53kppTih0fKJJgARIgAR8TYBC52uiLM9vBExi4tFZNF1sw+PHTjOf7vSpN5Bf4JDdJnR+nTWGYil0fntEWDAJkAAJhC0BCl3Ydr01G65SNze3hIGBKbS2OvHo0SCSEmOxd28+jr5VbolGUegs0U2sJAmQAAlYigCFzlLdxcq6CczPL8lK0TmzL2yXbCOmQ7KLSy7ZG7YEb7yRjfSMRPepIfeVQhdyXcIKkQAJkIDlCVDoLN+FbMCzZyO4d6/fROxycpLN/LoimV9XJClPNNVJZGRoJbCj0PGZJQESIAES8DUBCp2vibK8oBBYWVk1aU7On38oCydGkCERuqNHylBSkoEUmV8XGxsVMulBKHRBeUR4UxIgARKwNQEKna27N7wa53KtYnZ2Ef39ExKx68Otm32y20QyTp6olDQnOYiLiw4JIBS6kOgGVoIESIAEbEWAQmer7mRjlIAumnBK/rquzjEMDE5icHDapDapqck3iyeCLXYUOj6nJGAPAqurq6Yhvti9ZmVlBVNTUzLC8FR+Zg3KHtZRJvl4SkoKtwe0x+PyQiv02fHFc+NZKIXOkwZf24rAkiyS6Ggfxc1bPRgenpF9U+ORm5siw7DpMs8u1XwfjAZT6IJBnfckAd8SWFrS1fYDZj/m5ORkr6VrcXERT548QXd3N2ZmZiQVU6plhW5iYsKwmZ+fh4qLtiU/P19SS8VvKjH9/f1ma0Tl4T4SExORmZmJtLQ0I7ru9z2/6vkqw7m5uTLlJsPzo9d6rf2rfTE7O4vl5WWzq09RUZEEB5IQHb3xaI+2X9uhe3a7pV+v0Takp6ebZ0X7WHcM0mdHufjioND5giLLCHkC7e0jZguxmzd7TJSurq5I9lHNQqKkPImOjgzowgkKXcg/LqwgCWxIQH8RT05O4uuvv8auXbtQWlq66S/5DQuUD/UX/Oeff25+4ZeVlUHlwarHs2fPoFsc6p7V2i5tz8mTJ5Gdnb2ukLnb+sUXX+DBgwdQQYuMjDQCqJK2d+9eyWDwxrp7X4+Pj+Mvf/kL3n77bezfv39TcXTfb72v09PTpj9UzDRyqkL23nvvSUCgRH5vbJxF4fHjx+ZaFVqNwul/Km01NTXmedEtH3t7ew0f3c87JyfH6/pqOyh06/Um37cVAY3WzcwsYlQSE1+50oF2WRmbkBiDs2d3o7g43QzJBqrBFLpAkeZ9SMA/BFQeenp6zC/knTt3mqiQt8NnKg3nz59HeXk5Kisrjdj5p/b+L1WjWyozKr5fffWViXAdPnx4y0KnsqzyoxE5lTodfo6Li9tw72tfC50Ogc/NzZm6t7a24tatWzhx4oQR7a0Inf6cf/PNN02b3ZFJzzZoFO9///ufEVWVOpU8bw8KnbcEeb1lCOh0FxW73t5xdHeNo08WTzidM/IP1IHq6lz5y8k3fyVtBoRCtxkhfk4CoU2gs7NTFl7dQ1VVlRlK1GE499HR0WGidzqUVlxcDBUDjfLo8J2e73A4Xoky6Zy5+/fvm8iUlqVDcxqVqq2txcOHD02ESKM4fX195vrCwkIT1dEImNZlZGTEiIfeU4VQz1V50OPmzZumPhod03ro8GFWVpap2/DwsOTyHDJDgzpXz12/zYYU3W3dytcLFy6YYcuGhoYtC52K1KFDh8zQqcrcZofT6TT8rl27Zu6hw5oqXUeOHDFSqUPjKuA6BJqQkGD6TKOGbtHarHztA43GHj9+fMtCd/XqVRw7dszcS+/58qFt1HO0nhqNLSgoePmUbX9Pods2Ml5gBwLT0wvo7ZnA9evdcMkPXB16TU9LQGnZt/PrNH+dv46mpibzg6W+vt78cNa/QHmQAAlYg4AKkQ6pacTmzJkzr8zr0nlcKlkqDyoxKl0qYvoLXIcCVTZiY2NfaKxb6FTqVMo8he4///mPkS4d2tUy9DP95a/z0m7fvg2N9GidNEKokTGVOZUVHRrU4x//+IdZZOG+XocSVZI0+qXXaCRN54mpeGq0Ua/Vz3x1vI7QqWSqDKvcqgxpW3VenEax1oqErid0KoUq0jq8qf2h1yort2xrJPTlvlir3a8jdJcvXzZyrXVXadP/VKpVIvVnvg4p69C0yqY+E/pseHtQ6LwlyOstT6ClZRBffvkU1651y19g5RImL0KJDMMmiOTFxGj+Ot82sbGx0fyQr6urk3l8FVv6geLbGrA0EiCB1yWgc8JU6FpaWvDBBx9AI1uehwqSfnb9+nXoMGNXV5cRkQMHDhgZWy/ipEOu//rXv4xU6VwxjeTpoUKmwqLRuurqaiM4KiUqgf/+97+xe/du874Kw6NHj54vDNDhQRUYvV4jcfrzRstVWVJxVPE8evSo+RmksqNt0mFLHSbUOYFrHSp9+p97or/nOe6hUc/39PV2hU4jYVoXlVe9j0qdyp22c6M5eC8Pueq1Kq86J09FV/tCI5Mq2zqEqsO677///iv993L99fvtCp2KmgqdirIOO6s0qojv27fPROy0r/R9lX19TlRatb+8PSh03hLk9ZYnsLjokh8eSzJsMYNLl57KX00j8lduCt59d6dZOKFJiX156GRh/cesf72v9xenL+/HskiABHxHQOVKZUgjK9/73veMcHiWriKhw3s61KmROY0C6VCmRtXWkzm9fiOhU4HTCfkqAipOKiMqijrsqwKm91B5UzH77LPPzDkaPdSh03/+85/m541+r9EhFVIVujt37uCjjz4y0SEVD41k3b17FwcPHjTlebZJX6vI6XkaEVRp9Ty0XVr2WsK1XaHTsjV6pfdzR7F0qFjvcerUqVd4u+vxstApM43MqYxpRE7lVcvQMrWd33zzDX784x+b9m82SrJdoXPPIdQ26GuVb5U8Za8/93VYXJ8TlVadR6e/B7R/vT0odN4S5PW2IaDz6zR3XXf3OPoHJuQH17zZE3b/vgL5izVD/oryftKqwuIcOts8MmxIGBJQkWtvbzdRr3ffffcVwVCRUOHTf+caGdOpFbpCU4fVNjo2Ejq9TqOBbvFQqdK5ehqRUwHTSL8eKhAa5VNZOHfu3HOh088+/PBDI30qESp0Olz7ox/9yAxnqmio/OgcNK2vDr2+fOgfoaOjo+Y8vb/noUKiEUW97uUhzO0KnWe5ek8VaBUqZfrDH/7weeTS8zx9vZbQaTROU8HoELIKnR7KRtt+6dIlfPLJJ2Yo183VnLDG/21X6DyL0D5xC7guENFI3J49e0w99FnRhTB6/+9///uel73W6/8HAAD//7jSTM4AAC6NSURBVO2d55McV9XGjzbnnHNQzmm1kmwFB9mWARuDTQGuIlTZBMNXqIKCD/An2IQqqALetwxFMG8ZXLJcFsZryZKVc5ZW0uaszTnoPc8VLUbrnd2Z2ZnZ6Z6nq2ZntqfDvb97p/vpc889Z9E9XYQLCZDAAwKDg2Ny53aXnD/fLH39I5KWliD5+SlSVJQmxcVpEh0d+WBbXz4cPXrU7LZ161Zfduc+JEACC0igo6NDamtrpbW1Vfbs2SOJiYkPSjM5OSlNTU3S0NBgvh8ZGZHCwkKprKzUa0fxg+1m+tDf3y/vvPOOLFmyRJYuXSqpqalms7ffflsWLVokzz///IPdBgYGpLGxUY4fPy7r1q0z20dFRcndu3fl8OHDEh8fL0899ZRERkbK9P2Hh4fl0qVLcu7cOXnppZckJSVFBgcHpbm52Rxvy5YtpgwPTvafD1NTU9LX1yeoP7Z3XXBucCgqKtLrY7TrV3LgwAEZGhqS6upqyc7ONmV6aINZ/gFPnO/y5cty69YtU16Ly/Tdenp65M0335Rt27bJ2rVrDbO2tjY5c+aMxMbGmvVxcXECzqj/lStX5MUXX9Tre5rZdvrxXP/H+T/55BPZsWOHqWNCQoLr17N+trjV19fLxx9/LLt27ZJVq1YJpNfY2Ji8//77An579+6d9TiefLmIgs4TTNwmHAmMjU3I9Wsd8mHNTenqGpTFS7Lkke3lkpmZKHFx0RIT45uwo6ALx97EOjuFAATBtWvX5MaNG/LZz35WkpOTTdUgPnp7e+X06dMyPj4uixcvFgg63MjT09ONoIHAcrd4I+gmJiaks7NT3n33XSMUy8vLjYi7eRPXqi4pKCgQ64HRX4LOXblnWo/yjY6OCt4PHTokEJHr16+XjIwMwysmJkYgdCD0IGYgAsEG67At+EHw4B1CDuIZ3z/++OMPCWjXc0Ns/v3vfzfcIaAhMCMiIoyIggCGiML5IbghXnH8J554wu3x8D3aD2W4fv26nDp1SiB28/LyjNi2RB22QblRJ5QR+0GoYT0WMICwRD1QXxwD7WUJPdwPIDR3795ttp/PHwq6+dDjvo4mcP+CMqk/wnGpq+uWEyfq5eTJBtm8uVh2PFouy5bn+lR/CjqfsHEnEggJArgRw8Jz4sQJeeGFF4yFB9cKCLKDBw8aYVVaWip4YVusww1+8+bNs1qovBF0OB8EE0QChCUEA4RDUlKSES4VFRVGRALYQgg6iCYIW1gqIbRQXljJIN5g1VyxYoVAZME6lZ+fbyyYWVlZhiEEICygsEpie9SppKTE7INt3IliCEGcE0xgrYOge+6558x5cLw7d+4YZhBPON7q1atnbQ8cDxZQHA8iGQIN+0J8Qhw++eSTpj8eOXLElHv58uXGGot2gUUP67GgDrCYZmZmypo1a4wghBiEUITYh6UVVkcI3vkuFHTzJcj9w4JAf/+otDT3Sl19j148+/TCMKFPmnGyeVOR5OlwbEJCjMccKOg8RsUNSSAkCUAcnD9/3ogMWMOsGzSEDIQLhjEhRCBkWlpajNiCGMGNHUJlpgU3eAgg7IsXLD5YcNPHAhHiukAswuIDsYEhUFgIIThwHlgNISSwTN8f23V3d5tXWVmZESgQgzgWrH7YH+efzwKxhqFSiFSU01pQd9QDFktL0EB4QdCg7BC+sJ7B0oltYWEDT3wP6xrq5I6fa70gxrAthC3OD1GJOqOeEGQ4HgQWPrs7nmVZw74QadaC7VEWawgd7Yu6oE6oC8qBoW+sx4I6oC3RRzDkjPpgHcqIhwLsgz4EYTvfhYJuvgS5f9gQ0Guz/lin5MKFZh1yadcf7ZBe/BKltCRdivWVk5OsT48ReoGYHQkF3ex8+C0JhDoBiIO6ujojFODvhmE4LiTgKQGIPohW3AswPAxrLgTtfBcKuvkS5P5hSaBfJ0vcutWlPixXVMCNqxNxumzcWCwJ8dESFQ0Te5x5IpsJDgXdTFS4jgTsQ8C6IcNRHsNvuCG7s/TYp1YsabAIYPgWllX4POKBwB/WOZSdgi5YLcjzOIrA1BQcduFfNyb/+79vyrGjx80FPSExWn+cObJ9+1Z55plnZqwzBd2MWLiSBGxFAMNs7e3tZmgVw2bWEKetKsHCLggBCDoMS6PPYCjWGl6fb2Eo6OZLkPuHPYG33vo/9ftokbKyxXLpYqs0tw6q70axfP757SbUyfQwJxR0Yd9lCMABBOAfB58v+EPBUR/vXEjAEwKw8MJHD4IO/cZf1l0KOk/ocxsScEMAF/Wamhrzg9y69VGN7dQkV662ybDOjM3JSVJrXYqUlWYYX7uY2PtOyhR0bmByNQmQAAmQgM8EKOh8Rscdw50AxByesjA9HTOpqqqqzGyn0dEpDSVwVx1e69WsPqZxh3SK/Kp8ydQJFJgNe/z4MYPOihMV7hxZfxIgARIggfkToKCbP0MeIUwJQNBh6jliKSHwZU5OjomfVFBQKMuXr9Rp7ZVyq1YzTuis2L6+EZ2uny7PPrtSLl48Y4hR0IVpx2G1SYAESCAABCjoAgCVhwwPAhB0cIy+ozGpEMMJjtEQdseOHTOxnL74xRf1+0XqOI00PT3m1dk5JIMDN6WsPEl27ryf+guxiRCzigsJkAAJkAAJ+EqAgs5XctyPBJQAhlrhGA2nVsxUgsXujTfeMOteeeUVE0gSjq9IHXb1SpucPNUot2+f0fAmovkG10lpWbosXVKqw7Fp5EkCJEACJEACPhOgoPMZHXcMdwKw0CGCON4h2hB1HALv9ddfNxHSX375ZRNNHOutRTeV//mff6gfXb2kpZbLrt2LNQ5RtglKHK8x7CIi5ohKbB2I7yRAAiRAAiTgQoCCzgUGP5KANwQQSwjpf2Chy83NNRG/kermV7/6lTnMa6+9ZlLwTA9ncOjgYZNlIjt7sRz6+JaoIpSVq/Jkt4q7xESkhaGo86YduC0JkAAJkAADC7MPkIDPBOA/h9yLZ86cMb50ZZoXEUmhkSi7sLBQBdpuE59qeowhhC2ZmJjSCPPrpb6uW5o0R2xra7/mYxzTyRQ5msC5QFMJJftcLu5IAiRAAiQQfgRooQu/NmeN/UQAw6vwmYOVDkIOyZkxOQLvSOXiLr/j9Dh0ra19cuVKu1y+1Cpx8VGSlZ0khQWpUlKcZkKdID8sFxIgARIgARKYjQAF3Wx0+B0JBIDAdEFnnQJpxA4dqpUjh+9IhIq4Rx4pk5Ur8yQtLV5iNSgxhZ1Fiu8kQAIkQALTCVDQTSfC/0kgwATcCbr7ce3Gpbd3RK5dbdfwJ3UyNDwmjz5aIRs2FGooFIY2CXDT8PAkQAIkYFsCFHS2bToW3K4E3Ak6qz6Tk1PSfXdI6tS/rrGpRwb6RyUyapGZCbt5c4nGrOPECYsV30mABEiABO4ToKBjTyCBIBOYS9BZxYGw6+gYkOvX2o2wGx6ekOycZCkuSpOiolSNcUeLncWK7yRAAiQQ7gQo6MK9B7D+QSfgqaBzLRgmTpw82SD791+RsrIMgaVuzZp8DXMSowGNI+lf5wqLn0mABEggDAlQ0IVho7PKC0vAF0EHa93IyIQMaWiTU6cb5OzZJo1lNyzP7l1uwpxkZiUubKV4dhIgARIggQUlQEG3oPh58nAk4Iugc+UEa119veaGVf+6rs4BQYaJsrJMWb06X1JS4hiY2BUWP5MACZBAmBCgoAuThmY1Q4fAfAUdajI+PqkTJ4bl5Ol6aW8f0FyyYmbBlqh/XUlpuqSmarJYLiRAAiRAAmFDgIIubJqaFQ0VAv4QdK51aWrq1dywdXLkyB3NHZsmW6tLpXJxtiQkREtcXJSKPaYSc+XFzyRAAiTgRAIUdE5sVdYppAn4W9AhjdjIyLh0dw+rb12jHNbAxJgo8dSeZbJpc7EZkg1pICwcCZAACZDAvAlQ0M0bIQ9AAt4ROHDggPT390tVVZVJERYVFeXdAdxsDWHX1tZv8sM2t/SqwBvSLReZ2bBLl2ZrSrIEN3tyNQmQAAmQgN0JUNDZvQVZftsRCJSgs0DcuyeCYVhY6xCcOEtnwOblJRsfu1L1r0tIiOHECQsW30mABEjAIQQo6BzSkKyGfQj4e8jVXc1hsUNg4tMa5qS2tststmtnpeQXpJrZsPCv40ICJEACJOAMAhR0zmhH1sJGBIIl6GCpQ/y60dEJaWnulXPnm+XgwVtSXp4h27eXyZYtpTaixqKSAAmQAAnMRoCCbjY6/I4EAkAgWILOtejDw+PSqda6OzoE29bWp0GJhwSCb7NOmqiszJK0NIY5ceXFzyRAAiRgNwIUdHZrMZbX9gQWQtC5Qrtxo0MuXmqRO7fuSlZOopSWZJj8sNk5SfSvcwXFzyRAAiRgIwIUdDZqLBbVGQQWWtCB4sTEpHR2Dsp7mhu2r39UclTMrViRI0WF6ZKs2SYQ9oQLCZAACZCAfQhQ0NmnrVhShxAIBUGH4dapqSmTGxapxM6da5aTJxukqDhVHn9sqSxbniORkREOIc5qkAAJkIDzCVDQOb+NWcMQIxAKgs4VydDQmHRo+jCEOGlV/7q2tgG10sXK+nWFarXLldhYzoZ15cXPJEACJBCKBCjoQrFVWCZHEwg1QWfBHhublFu1nXL6TKOZNJGRkaBDsclSVpohefnJkpQUa23KdxIgARIggRAjQEEXYg3C4jifQKgKOlfyEHYf1tyUixdbZOOGItmwsUiKitIkMTFGoqIimB/WFRY/kwAJkEAIEKCgC4FGYBHCi4AdBN34+KQMDoxJe0e/XLrUKvX13Sa7xLN7V0pBYSrzw4ZXl2VtSYAEbECAgs4GjcQiOouAHQQdiN/TmRMISgz/uoaGHqlTUYfME/n5KbJqZZ6sXJXnrIZhbUiABEjAxgQo6GzceCy6PQnYRdC50u3X0CYNKuhOnGqQ8bEJ409n/OvKMiQ3N9kMxbpuz88kQAIkQALBJUBBF1zePBsJyOHDh03IkOrqaomOjradP9p5TSF26FCtnD/fIjt2VMimTcUmMHGs5oaNiorU+rCRSYAESIAEgk2Agi7YxHm+sCewb98+6e7uViG0SdNuVWoQ3xhbMRlTC93Q0LgZfq356KbxtStUv7pNOnGiuCRdRSqDEtuqQVlYEiABRxCgoHNEM7ISdiJQU1OjvmmjsmXLFklNTdXJBvYL4IvAxBB2dXV3VdgNCoITw9cuKztJ1q0rkBIVdoxfZ6deybKSAAnYnQAFnd1bkOW3HQE7+tDNBnlgYFTj13XJ+QvNarkbU5EaL/l5KSrq0qRQQ53QYjcbPX5HAiRAAv4hQEHnH448Cgl4TMBpgs6qOGbEXtYQJx98cEN6eodl9eo82VpdJhmZCSbMCYWdRYrvJEACJOB/AhR0/mfKI5LArAScKugQ5gTZJoaHx+X27S45caJOc8S2yNatZfLII+VSUZE5Kxd+SQIkQAIk4DsBCjrf2XFPEvCJgFMFnSuM/v4RaWrqlXqNX9ffN2Li2cFCV1VVrGFOUhiY2BUWP5MACZCAHwhQ0PkBIg9BAt4QCAdBBx6Wxe7mzQ65fr1DWlr6JDs7UQryU81s2MLCNImMZIwTb/oOtyUBEiABdwQo6NyR4XoSCBCBcBF0rvj61Ep380aHvPfeVRHVcMuW5Uj1llJJSY2ThIT7+WFdt+dnEiABEiAB7whQ0HnHi1uTwLwJhKOgm5q6J8gPi1mw1662y/Hj9XL5Spvs2lUpj6p/HeLXcSEBEiABEvCdAAWd7+y4Jwn4RCAcBZ0rqO7uIWlu7jP5Ydvb+3TYNULy1K9u8ZIsQYBiZJvgQgIkQAIk4B0BCjrveHFrEpg3gXAXdBbAkZFxOXumSZpaemVEZ8bGx0dr/LpUKS1N1wDFiZpBI8ralO8kQAIkQAJzEKCgmwMQvyYBfxOgoHuYKAITX7zQIkgjhlh2yA27alWeTqBIMv51ERGcOPEwMf5HAiRAAp8mQEH3aSZcQwIBJUBB9zBe+Nchfl2fBiO+Wdsphw/floGBMVm7Nl+efnq5JCXFPrwD/yMBEiABEvgUAQq6TyHhChIILAEKupn5Qtj1qqhr0Nh1iGHX1tYnXV2acWJNnqxelW/862bek2tJgARIgAQo6NgHSCDIBCjo5gbe2TkoV3UW7OkzjZKWFi85uUmSkZYgZeUZ5n/6183NkFuQAAmEFwEKuvBqb9Y2BAgcPnxYpqampLq6WhPXR8uiRfQRc9csk5NTcvJkvZw61aCBiftNmJPFi7P/419Hdu64cT0JkED4EaCgC782Z40XmMC+ffuku7tbnf83SWVlpc7mjFngEoX26UdGJnTodVBuqX9dzUe1Eh0TKevWFhhxh5mxFMSh3X4sHQmQQHAIUNAFhzPPQgIPCNTU1OhszlHZsmWLpKamSkRExIPv+GFmAghKjGwTdXXdGsOuV1rb+mVocExWr1b/utX5kpOTPPOOXEsCJEACYUKAgi5MGprVDB0C9KGbX1tgwsQV9a/DKykpWoqK06WwIFWys9TPLjPBBCqe3xm4NwmQAAnYjwAFnf3ajCW2OQEKOv804KBa6Gpqbsjt210SFR0pS5dky4rleZKaFiexsVEUdv7BzKOQAAnYhAAFnU0aisV0DgEKOv+05T0NczKsGSb6+kfNjNhPjt7ReHYTmhu2QtZvKJTMzET/nIhHIQESIAEbEKCgs0EjsYjOIkBB59/2nJiYkrt3h6Re/euamnukvX1A88FGSHlZplRtKTHZJjiR2L/MeTQSIIHQI0BBF3ptwhI5nAAFXWAaGMKuvb1fzp9vNoGJkTIsS/3qkBu2qChNMjISAnNiHpUESIAEQoAABV0INAKLEF4EKOgC394tLX1y4kS97H/vivrV5UrV5hJZsjRbEhNjNExMJP3rAt8EPAMJkECQCVDQBRk4T0cCFHSB7wOTaq0bGZ2QoaExuXSxVc6p1a5VRd7evStklYY6oX9d4NuAZyABEgguAQq64PLm2UhAKOiC2wk6Ogakob5H6urvan7YfuNTV1mRKWvXFajFLlbjADJTR3BbhGcjARIIBAEKukBQ5TFJYBYCFHSzwAnQV2NjkzpxYlBOaBqxDp00EREZocGIk6RYfetKStI1wHN8gM7Mw5IACZBAcAhQ0AWHM89CAg8IUNA9QLEgH5Bt4vixOrWU1kl5Rbps316uKdiyTOw6xK9jKrEFaRaelARIYJ4EKOjmCZC7k4C3BCjovCXm3+0xG3ZkZFzz6Q7LSbXY1dd3C3LCrlldIBs2FkpcXLR/T8ijkQAJkEAQCFDQBQEyT0ECrgQo6FxpLNxnCDtMlOjqGpRmfW9s7DGzX5EbdsmSLElPZ5iThWsdnpkESMBbAhR03hLj9iQwTwI1NTUyOjoqVVVV6ruVqiIicp5H5O7zITClGScg5s6ebTLvSUmxkpeXbGLXlZVlGIsdJ07MhzD3JQESCAYBCrpgUOY5SMCFwL59+3S4r1s2b94sFRUVGhctxuVbflwoAsZi19orH354U+7cuauBiBNl584Kyc9PleTkWONjt1Bl43lJgARIYC4CFHRzEeL3JOBnAkeOHJHJyUmprq6W6OhoOuH7ma+vh7t3T7Rdpkx+2OamXjl/oUk+OnhLVq3IlUc0PyzCnHAhARIggVAlQEEXqi3DcjmWAH3oQr9ph4fHTXgTzIjt6R0yEyhGRybUqlosFZWZDHMS+k3IEpJA2BGgoAu7JmeFF5oABd1Ct4B35799u0suXWqVmzc7NTdsovrXpUhxcZrxscPsWPrXeceTW5MACQSGAAVdYLjyqCTglgAFnVs0IfsFAhN3dPTL/v1XBXliMWli29YyyS9IUf+6OJMfNmQLz4KRAAmEBQEKurBoZlYylAhQ0IVSa3hWFsu/DrlhGxowI7ZRzp5p1sDEmfLkk0tl6dJszw7ErUiABEggQAQo6AIEloclAXcEKOjckbHH+sHBMWnXnLB1GpAY1jpMpEhLi5dSTSG2bFmOxGi2CS4kQAIkEGwCFHTBJs7zhT0BCjpndIGxsQm5fr1DzMSJniETlDgnJ9nkhs3NTTahTpxRU9aCBEjADgQo6OzQSiyjowhQ0DmqOU1lanXCxL8/vCHXrrbLmrX5sn59kZSWpktiYoxERUUwNI3zmpw1IoGQI0BBF3JNwgI5nQAFnfNaeHx8UgYGRqWttV8+OXrHZJzI1Bmxe59ZoYGJU5gf1nlNzhqRQMgRCKigm5iYUB+TFvUvSdPhh+SQq3ywCtTR0WFOlZ0dvo7T/f390tPToze3fLVYhLeP0YEDB0x/2LNnT7C6YMidx4n94Z7OnBjRWHVNmkasQV/wr2tvHzATJ1avzJPKxVkPtQOvj//F4cT+8N/a8RMJBIdAQAUd8lVeu3ZNCgoKNH7TwxezmaqH6Pm9vb2SkJCgT7RxM20y4zpcDLB4IxpHRkZkaGjIq1yavpbv9u3bpnzl5eXm3ZM/wSyft/y83R717ezslObmZnUaX6YplGI9QWCyKTixP/zzn/809X/uuec84oCNvO0P3m6Pc/jav9kfQO9hfmNjYnzrTp1sMEOuySmxkpIcL2Vl6ZKj/nUYivX2+nj/LCK+8LZLf1i+fLlfUuGNaQP09fWZa05SUpLyTpSpqSmpr6/X+IFFkpOTY7K0WEz5TgJOIBBSgs7XC5wvgskXgcHy3e/y5H2fg6/9wRdB521/9XZ71MjX+rA/zN4frlxulUMf35bTpxtNbtj16wqlsChNJ1Hck9ra61JYWOjRA+/9s4g4mbe/BB1ELzh98MEHgpERMF60aJF89NFH8thjj8mmTZuMyLOY8p0EnECAgs4LixFvePe7vJNvKN5YEH3tDxR0vllsfeW90P0VQYkR6qRNQ50cPHhTWpr7jKB79NESXd+mkyeKKej+Y8H3l6CDNW5gYEBOnjyporlWs3lEyOLFizVe4FLjAoRRAqzjQgJOIkBBR0Hn9RP/Qt8g5/oBhnr5KOjCS9Chv8K/bnR0Uodh70qjBiZuae3T/LD9OhzbKzt2rFNXhBIdAoycq2ub70O9f8+nfP4SdAA1Pj6uk1Ma5R//+IcZXv3iF79orHWRkZ5x9qgxuBEJhBABnwUdTNqWs7+7+lhOv+np6QI/hrkWb7e3jofhJSye+OlZ++Dprbu72ysnfZbvPj3yvs/B1/7w4YcfGn+1Rx991BwoOjpah99mv8l421+93R4F8bU+7A/e9Ye+vhG1GnXKxYvNMjbeJxVlBZobNlvS0hMkXV+RkYvuH9DN33DkDf9obyeVoT/jHvWHP/zB+GV///vfn/N35gY5V5OALQj4LOgaGhrkzJkztqgkC0kCoUTg/Pnzxl+toqLCFAsPO55OFAmlerAs8yMwMTGlacS65datLjMkm6Firqw8UydqxemksCiPLXbzK4U99i4pKdHYfus9LiwsorDQwVr4l7/8xUyYe/XVV42lDg9QHG71GCU3tBEBnwUdnn7g08KFBEjAOwLHjx83Q3BVVVVmRzhr48Ul/AhA1CGG3W0VdYeP3JYLF1qkqqpYtm8r/1SYk/Cj898aI9SRpw898J/DC1EM4EN37tw5M0K0bds2Y6FD1IXU1NT/HpyfSMAhBHwWdA6pP6tBAkEnwMDCQUce8ifEMCzi19XrC8GJx1TkZWTES9XmUh1qTDIWu5CvRIgU8MqVK3Lnzh0T6mfJkiU6GaXNhC+BxW7Dhg0CyzgFXYg0FovhVwIUdH7FyYORwNwEKOjmZhSOW1iBiS+cb5EbtR3S1zusYi5ZCgtSpUTTiBUW0qrkSb9A7FMIOowibd++XYaHh3Vou8EIu7Vr10pubq7Ex8d7cihuQwK2IkBBZ6vmYmGdQICCzgmtGNg69PQMm7yw7713RWJio2TVqjzZsqVUkjQgcVx8tAlWHNgS8OgkQAJ2I0BBZ7cWY3ltT4CCzvZNGPAKTE3dE8SvGxoak8uXWuXosTq5erVNnnlmuWzbVqbWurSAl4EnIAESsBcBvwo6+CjU1dXJzZs3zYQJROdes2aNW2dWhD5BTK7BwUHjFI6ZRykpKfokukWDbZbai6RLaZHi6tatW9LU1CR5eXmyYsUKk2rGZZOHPiIdDfw8MDSAlDVIS+NpurSHDhRC/9y9e9cMe8AxGXVC6h30B/CYKZcrhkkQzgN9ABMEYmJiDIddu3aZkAMhVLV5F8Xpgs7b/ox2v379+oOZh+grCAC7efPmebNeqAMgZR2G/VAvXNPgtwV/LnfLbL+X3t4xaW7qVf+6bunQ3LAQevn5KbJhvf6e9D0qKrQD5Hp7Pfz3v/8tN27ccFR/cNfuXE8C/iTgd0GHi/nHH39s4v+UlZXpE+UzbmPQ4SL2i1/8wvgzIFadJegw+8/Ogq6lpUXOnj0rp06dMgJm9+7dJkr59Ia7H2x01AiZrq4ujUVVbEQd4uMh3yDilNlx9iME3OXLl+WTTz4xN2bMOENeRbyjP8yUcxczP//2t78J8t1CzGFGG+JO7dy5k4JuescJ0f997c9/+tOfjPBBn8diCTqkZ7LrAkGHB1uIE/hrIeSGFXdwep08/b0MD4/rNaVBj9spY6MTkp2T9MC/LjMzMWTDnHh6PbS4/PGPfzSCzkn9waob30kgkAT8Kuisgh48eND8IHHjfvbZZ90KOtzk3377bWORQ4RwJy14wkTeQIjUHTt2zPh0Dqfd1tZW+etf/2puYq+88ooRdL/5zW+MkHvttdeMuLGbqEPg00OHDmmao4Pyox/9yAg4WGHQ1j/96U+N9XF6IN2rV68KRN0LL7wwo+BzUt9wqoXO1/6MfJtYnnjiCSc1s2AE4t133zUpqGBxxHVgpsXb3wv8686fb9bfWK05XJX61q1YnqtBieP14SdGrzmhFwLHk+uhxQb9Ade8xx9/3FrFdxIgAQ8IBEzQ4ekUAVPdCTo8zUPQHThwwDy9Is+ekxZcwCBqsLgTdBhixc0dsZLwNPqVr3zFWLHeeOMNczN4+eWXzXoEwrTTgsC5EGd4Mv/e976nN5p0Y6l488035Tvf+Y4ZgsYwlLXAcof+cuHCBXn66afdPgBY29v93amCzpf+PDk5KUeOHDEPPo888ojdm/ah8iNbhyXoMNzqTtB5/3tBGrEJ6e0dkevX2uWCZpwYGZnQh8YsFcXL9OEw5qFyhMI/nlwPUU4n94dQaAeWwdkEAiLoIGTwA55N0OFpHsOM77zzjhmWxLBET0+PETAQd5mZmbYm78kFDBd8CFpEM6+srJTnn3/e1Pm3v/2tGbLeu3evrFy50q0PYqgCwg0awTzhU/m1r33NJMNGn/jzn/8sn//8542Ad03j4zrktGrVKiP0YdlEdHhYNjAE66TFqYLO2/5sDdFiWBJuBnDRwEMAUvhh6N3Obhfor54KOm9/L9ZvYXJySnq6h6WtvV/9dXs1b2mPEXkrVuSaWbFFRaEzccKT6yH6w8jIiHFBcWJ/sNqN7yQQKAJzCjo8MUF84X36ArO4lYfSdVjQU0EHP5Njx44ZHxOcA4mUMfyAoRdMpggVyxQsSCgfXjMtcPLHCyLEWjy5gGFIZt++fWZCBJ7gYc3EgtyDGIp97LHHZN26dRpUNM467IK942KLPgCRhs/TF9Td6gsYar548aJh8uUvf9kE8cRNCz5ye/bskY0bNxoRbx0Dgg6TaS5dumQmQiD/Im7s4P7SSy9pgNUMR+VgdKqg87Y/W4IO/qZ4mIOLBnxw0f4Qd/C3RJ9yvbZYfcYO754KOm9/LzPVvaNjQH8/rSbTRHx8lP6OkqUgP1U5pktKarw+FM2eK3imY/pznSfXw9n6AwQ+rPd27g/+5MljkcBMBOYUdBhGwdMSZitOX+AHhZttQkLCQ+LLE0GHHy8EEp7IrJQumBX285//3PhR4cbvOiw3/dzB/B+CAzcrcJhpQdRx3IxchZcnFzBc8Pfv329mw0LQfeYznzGH/93vfmdE3pNPPmmEretxZzp/MNahrdAXYFWdSdjCwpqWlmbE+eHDh83wKcqFYWPwwTr4CuImDUGH4J7WAuEGxhCLcIhHn3j//feNAPzxj39srJehwMAq73zfnSrofOnPeEhAe+OBANcB/M5++ctfGjH/3e9+1/Sp6f6W8+UfrP09FXS4XsLdAIsnvxd35b8viCaNb92ZM036ex2XXTsrpKIyS62eifrbjFFx7G7vwK735HqIEszUHzBxDnWze38ILGEenQRE5hR0CKeBkBJ4n77gAowhwfz8fHMjtr73RNBhW/xI8bKewHGOn/zkJ7JbZ4XCSofjhsICXz+ITXCYacFwKSwKELfW4skFDCLZejrH/rBGYcEFDOLxxRdfNGImFIYcIeba29vVGfu8uQFb9bTeMYSK4VGEXLFm+MLq8q1vfcv40GFSBHzovv71rxuRCr8618XqC7ix4zMco7H9t7/9bdPHnJSqx6mCztf+jPbGgusAxP3rr79uht0hbjDsHiqWetf+6slnTwUdfGgxI96b34u784Pl8PCEjnQMSK3Ohv3oYK2ZKLFhY6GKu8XKMnJBRJ0n10OrTjP1Bwj9r371q7buD1b9+E4CgSIwp6DDjRwXGncWOtyYYVVxjS02k6DDjxQWGMQkgvDBkxjitOEGjphr8LdDepaf/exn8rnPfU5gnQqVm7hloQOHmRbLQmdZGrGNuwsYblgQRrh5gV1tba1xnMbnb3zjG8ZS9etf/9pYwV599VVjpQSjhV7QXp5a6DB0DovcmTNn5Ac/+IGpAwQdhlx/+MMfmovy6OioEa2ITQchj+F3CFcIWzD617/+ZSx62B+C2UmpeuA3iRsUwvPgocX1t7PQ7Tyf8+N3Mld/xu8cbhVW/4f/KCy+6P9ggT6GBxqsQ/+383C7O0GHayEeEvHQhv4P94rZfi/wJXS9tnjSRohVh9RhdXXd0tzSK12dg5ofdkqWLc3WB6Q8E/LEk+P4axtPr4eu/QExK9EfYLF1Qn/wF0sehwTcEZhT0Lnbcab1uOnjxoxwFdYsVwyxWcFkEXcON2okSMakBwTfhe8UbuIQRbix19TUyFNPPWWCitr1yRw3a/iDIR4fFsSfgrM/bma4QCE+G0QaZvXhf8yEw7CTlXcQT+u4kWGSRCiIuZnaerZ1EP+nT582s3zR/hAsuNHjYg0LHYbocYGHnx0mfuDGhr6A/gHfSQh/WEOxzTe/+U0Tj86uw24zcXKqoIMQh4iBX+hM/fm5554zAcet/l9dXW36BazfECwQ7pZfLYbvv/CFL9gybA/aHPWHUHvvvfcME0z0QkxFXOcgThBw2Or/+H3Aqo0H4Zl+LxC71ijGTP1prnWYLHHtarvcrO1UzlFm+BX5YYtL0lVIx6t/amAfGOe6HsK/FgwQUB7Xien9ARZtXA8R0ggPffNhMRcrfk8CdibgV0GHJ3TcmPEDhHMzbtwQM8uWLTMWFljgfv/735uLFkQdbuQQM/A/gwUGVhs8jWLoDjPd7LqgnpjlCVGDBT5jmNwASyRuWG+99ZYZRkKYEtzIEIQXwhYZMyDwwAA3Nyuwph05wBILvyCrTriRwU8Qzs1oZ/QRDDfDLwZCF3HocKOHuMf36A/4jL7jrXUi1Hk5dcjV4o6HmZn6Myxwrv3/S1/6krFIox9gIgQe/PA93tH/0VfsuuDahocSPNThAQdDx1u3bjUZI6b3f/iTwmrv7vfiL5eLwcExdWW4LqdON0qcCrvtmkJs6bIc9VOMl9gYndQVuSgguD29Hs7WHyCIcT3gQgIk4J6AXwWdNayKCxasLLAuwZndeqrCkymGGiD0cJPGEz1u+NgOL+yPJzVY5uxskUE9wQAvLKgrXqgbrJioMxYIWTxtQghjH/BwZYDt7bqgPqgX6oN6oX3RD1AnrIMFAy9MfMF32Bb/o+3xPbjgM15OeyJ3uqCbrT9P7/9oazzEYD1+8+gr6CN4oe3tuqAeVp/GZ9QF1wC8T+//qDfq7+734q/+P6X5YTFR4u7dQblypU1jRdabsuzcUSlr1xUaa10geHtyPUQd8WDn1P4QCK48JglMJ+BXQTf94PyfBEjg0wScLug+XWOuCSUC4+OTKuqGpB7+dc290qETKDBZorw8U/06S9Q6bl8hHUqcWRYSCDYBCrpgE+f5wp4ABV3Yd4GQADAxMaV+y/061NtshB1ShmVlJUlJcboUFqWqn3NiSJSThSABEvCMAAWdZ5y4FQn4jQAFnd9Q8kB+ItCsmSaOHqvTSRxX1Ic5R6q3lMjKVXkmjVgM/OtCMD+sn6rOw5CAYwhQ0DmmKVkRuxCgoLNLS4VPOWGtG9V8sINDY+pbd0etdi06mWNCPvPsClm2PEf96xLCBwZrSgI2JUBBZ9OGY7HtS4CCzr5tFw4lh19dff19/7p2HZLN1GHYSs02sUxnxMK/jta6cOgFrKMdCVDQ2bHVWGZbE6Cgs3XzhUXhR0fvZ5s4eaJBBjTcSVRUhOaEjTP+dcXFaTo7feHzS4dFQ7CSJOAFAQo6L2BxUxLwBwEKOn9Q5DGCRQDZJo4evSOf6GvpkmwNAFyi8fSyTEqx2FikEgtM/Lpg1Y/nIQGnEKCgc0pLsh62IUBBZ5umYkGVAPzrRkYQv25IjunEidOnGjWGZqxm9FmmmV0KJDbOvvEy2cAk4CQCFHROak3WxRYEKOhs0Uws5DQCEHaYDWv861r6pKd7SKI148S6NflSuThL05rFT9uD/5IACQSTAAVdMGnzXCSgBCjo2A3sTACBiRsaejS9YZO0qLCDb11+booUFqZKWXmGZsSI4jCsnRuYZbctAQo62zYdC25XAhR0dm05ltuVwIQKuya12H1Yc1PqVeDl5iTKzp2LJScnWdN4xRhh57o9P5MACQSWAAVdYPny6CTwKQIUdJ9CwhU2JKBpeE0O2uGhcWlUYXf2bJN89FGtrFiRKzt2VMjGjUU2rBWLTAL2JUBBZ9+2Y8ltSuDAgQPS39+veTOrJD8/3ySit2lVWGwSMASGNCBxe/uA1N3plta2PunrG5HIyAjZvKnYDMOmMMwJewoJBJwABV3AEfMEJPAwAQq6h3nwP2cRuHq1TS5fbpPGxh7NB5sgRUXpGr8uTfLyUyROZ8QyzImz2pu1CR0CFHSh0xYsSZgQwJArbmrV1dVhUmNWM9wIIDAxJkzs339ZBgfHBcGIN28qkqzsJJMfNioqMtyQsL4kEHACFHQBR8wTkMDDBCjoHubB/5xH4J462CHMCYZiG3XCRO2tLvOelZ2oDzKlUlqa4bxKs0YksMAEKOgWuAF4+vAjQEEXfm0ezjUeGBiV7u5h6VAfu+aWXiPsUtPi1Ye02Ai76Gha68K5f7Du/iNAQec/ljwSCXhEgILOI0zcyGEExsYm5datTjl5slGHYUeltCxdsjOTJDcvWTIyEkwqMYdVmdUhgaASoKALKm6ejATuBxamDx17QrgSwHBsveaHPXGywUycWLo0W5YtzZH8ghSJj4/mpIlw7Ris97wJUNDNGyEPQALeEaCFzjte3Np5BBCUeGBwTFpb++TatXYT5gQBiRG/LiEhxnkVZo1IIAgEKOiCAJmnIAFXAhR0rjT4OVwJTE3dk+HhcenqGpSuzkEZHZuQ9euLTGiTcGXCepPAfAhQ0M2HHvclAR8IUND5AI27OJrAoFrr+nqHTdqwyKgIR9eVlSOBQBGgoAsUWR6XBNwQoKBzA4arSYAESIAEfCZAQeczOu5IAr4RoKDzjRv3IgESIAEScE+Ags49G35DAgEhQEEXEKw8KAmQAAmENQEKurBuflZ+IQhQ0C0EdZ6TBEiABJxNgILO2e3L2oUggSNHjsjk5KTJ5RodzbhbIdhELBIJkAAJ2I4ABZ3tmowFtjuBffv2aSqkbtm0aZNUVlZKTAzjbtm9TVl+EiABElhoAhR0C90CPH/YEaipqZHR0VHZsmWLpKamSkQEwzSEXSdghUmABEjAzwT+H5wqaxoFwROwAAAAAElFTkSuQmCC" } }, "cell_type": "markdown", "metadata": {}, "source": [ "## Problem 4\n", "\n", "This problem concerns the *parametric* forms of solutions, as presented at the end of section 1.1 in the online textbook. \n", "\n", "For parts A -- C, state (i) what shape (point, line, plane) the solution set has, (ii) the *Degrees of Freedom* in the solution set, and (iii) whether the given point is in the solution set. \n", "\n", "(Optional: on your own, try to imagine what the solution sets looks like graphically.)\n", "\n", "(A) Solution: $(x,y) = (a,0)$ for any $a\\in \\mathbb{R}$. Point: $(0,0)$.\n", "\n", "(B) Solution: $(x,y) = (a,-2a)$ for any $a\\in \\mathbb{R}$. Point: $(1,0)$.\n", "\n", "(C) Solution: $(x,y,z) = (a,b+1,a+b)$ for any $a,b\\in \\mathbb{R}$. Point: $(1,10,10)$.\n", "\n", "For parts D and E, for each of the graphs, give (i) the equation for the line in the form $ax+by = c$, and\n", "(ii) supposing this is a graph of the solution to some set of equations, give the parametric form of the solution\n", "in the same form as in parts A -- C. \n", "\n", "(D) \n", "\n", "![Screen%20Shot%202021-07-08%20at%2010.53.59%20AM.png](attachment:Screen%20Shot%202021-07-08%20at%2010.53.59%20AM.png)\n", "\n", "(E) \n", "\n", "![Screen%20Shot%202021-07-08%20at%2010.51.22%20AM.png](attachment:Screen%20Shot%202021-07-08%20at%2010.51.22%20AM.png)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Solution:**\n", "\n", "(A) Line, 1 DOF, yes.\n", "\n", "(B) Line, 1 DOF, no.\n", "\n", "(C) Plane, 2 DOF, yes. \n", "\n", "(D) $5x + y = 5$\n", "\n", "(E) $-2x + y = -4$ or $2x - y = 4$ etc. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Problem 5\n", "\n", "For each of the following, state whether the given matrix is in \n", "\n", " (E) Row Echelon Form, \n", " (R) Reduced Row Echelon Form, or\n", " (N) Neither.\n", "\n", "\n", "(A) $\\begin{bmatrix}\n", " 1 & 1 & 0 & 1\\\\\n", " 0 & 0 & 1 & 1\\\\\n", " 0 & 0 & 0 & 0\\\\\n", " \\end{bmatrix}$\n", "\n", "(B) $\\begin{bmatrix}\n", " 1 & 1 & 0 & 0\\\\\n", " 0 & 1 & 1 & 0\\\\\n", " 0 & 0 & 1 & 1\\\\\n", " \\end{bmatrix}$\n", "\n", "(C) $\\begin{bmatrix}\n", " 1 & 0 & 0 & 0\\\\\n", " 1 & 1 & 0 & 0\\\\\n", " 0 & 1 & 3 & 7\\\\\n", " 0 & 0 & 1 & 1\\\\\n", " \\end{bmatrix}$\n", " \n", "(D) $\\begin{bmatrix}\n", " 0 & 1 & 1 & 1 & 1\\\\\n", " 0 & 0 & 2 & 2 & 2\\\\\n", " 0 & 0 & 0 & 0 & 3\\\\\n", " 0 & 0 & 0 & 0 & 0\\\\\n", " \\end{bmatrix}$\n", " \n", "(E) $\\begin{bmatrix}\n", " 1 & 1 & 2 & 1\\\\\n", " 0 & 0 & 0 & 0\\\\\n", " 0 & 0 & 0 & 0\\\\\n", " \\end{bmatrix}$\n", "\n", "\n", "\n", "\n", "(F) $\\begin{bmatrix}\n", " 0 & 0 & 0 & 2\\\\\n", " \\end{bmatrix}$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Solution:**\n", "\n", "(A) R\n", "\n", "(B) E\n", "\n", "(C) N\n", "\n", "(D) E\n", "\n", "(E) R\n", "\n", "(F) E" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Note\n", "\n", "For the following three problems, you will need to trace the evolution of the matrix as you perform Gaussian Elimination. You do not need to format these in Latex, you may simply choose to indent your entire answer, or you may inclose it in the HTML tags `
` and `
` to get preformatted text, like this:\n", "\n", " 1 3 5 7 \n", " 3 5 7 9 \n", " 5 7 9 1\n", "\n", " R2 = R2 - 3*R1\n", "\n", " 1 3 5 7 \n", " 0 -4 -8 -12 \n", " 5 7 9 1 \n", " \n", "etc. OR:\n", "\n", "\n", "
 \n",
    " 1  3  5  7 \n",
    " 3  5  7  9 \n",
    " 5  7  9  1\n",
    " \n",
    "R2 = R2 - 3*R1\n",
    "\n",
    " 1  3  5  7 \n",
    " 0 -4 -8 -12 \n",
    " 5  7  9  1 \n",
    " \n",
    "
\n", "\n", "Hint: We've designed these problems so you get integers throughout the computation -- not the usual situation, but easier for hand computation!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Problem 6\n", "\n", "Consider the following matrix:\n", "\n", "$$\\begin{bmatrix}\n", " 1 & 3 & 5 & 7\\\\\n", " 3 & 5 & 7 & 9\\\\\n", " 5 & 7 & 9 & 1\\\\\n", " \\end{bmatrix}$$\n", "\n", "(A) Use the elimination algorithm from lecture to convert this matrix to reduced echelon form. Show all work (including the matrices at each step) and put a box around the pivot positions in the final matrix,\n", "\n", "(B) List the pivot columns, and\n", "\n", "(C) State whether this system is consistent or inconsistent and why. \n", "\n", "\n", "\n", "Hint: To enclose a number in Latex in a box, use the Latex command `\\boxed{...}` as shown here:\n", "\n", " $$\\begin{bmatrix}\n", " \\boxed{1} & 0 \\\\\n", " 0 & \\boxed{1} \\\\\n", " \\end{bmatrix}$$\n", " \n", "$$\\begin{bmatrix}\n", " \\boxed{1} & 0 \\\\\n", " 0 & \\boxed{1} \\\\\n", " \\end{bmatrix}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Solution**\n", "\n", "(A)\n", "\n", "\n", "Running Gaussian Elimination\n", "\n", "\n", "Creating Echelon Form\n", "\n", " [[ 1 3 5 7 ]\n", " [ 3 5 7 9 ]\n", " [ 5 7 9 1 ]]\n", "\n", "R2 = R2 - 3*R1\n", "\n", " [[ 1 3 5 7 ]\n", " [ 0 -4 -8 -12 ]\n", " [ 5 7 9 1 ]]\n", "\n", "R3 = R3 - 5*R1\n", "\n", " [[ 1 3 5 7 ]\n", " [ 0 -4 -8 -12 ]\n", " [ 0 -8 -16 -34 ]]\n", "\n", "R2 = -(1/4)*R2\n", "\n", " [[ 1 3 5 7 ]\n", " [ 0 1 2 3 ]\n", " [ 0 -8 -16 -34 ]]\n", "\n", "R3 = R3 + 8*R2\n", "\n", " [[ 1 3 5 7 ]\n", " [ 0 1 2 3 ]\n", " [ 0 0 0 -10 ]]\n", " \n", "R3 = -(1/10)*R3 \n", "\n", " [[ 1 3 5 7 ]\n", " [ 0 1 2 3 ]\n", " [ 0 0 0 1 ]]\n", " \n", "Back Substituting\n", "\n", "R1 = R1 - 3*R2\n", "\n", " [[ 1 0 -1 -2 ]\n", " [ 0 1 2 3 ]\n", " [ 0 0 0 1 ]]\n", " \n", "R2 = R2 - 3*R3\n", "\n", " [[ 1 0 -1 -2 ]\n", " [ 0 1 2 0 ]\n", " [ 0 0 0 1 ]]\n", " \n", "R1 = R1 + 2*R3\n", "\n", " [[ 1 0 -1 0 ]\n", " [ 0 1 2 0 ]\n", " [ 0 0 0 1 ]]\n", "\n", "$$\\begin{bmatrix}\n", " \\boxed{1} & 0 & -1 & 0\\\\\n", " 0 & \\boxed{1} & 2 & 0\\\\\n", " 0 & 0 & 0 & \\boxed{1}\\\\\n", " \\end{bmatrix}$$\n", " \n", "(B) The pivot columns are 1, 2 and 4 \n", "\n", "(C) The system is inconsistent because of the last row, which is a contradiction:\n", "\n", "$$0\\cdot x_1 + 0\\cdot x_2 + 0\\cdot x_3 = 1$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Problem 7\n", "\n", "Find the *unique solution* to the following set of equations by using the Gaussian Elimination algorithm by hand (the *solution* is\n", "the listing of the values of each of the variables, not just the reduced echelon form). Show all work, including each matrix that results after the row operations. \n", "\n", "$$\\begin{aligned}\n", " 3x_1 - 3x_2 + 9x_3 &= 24 \\\\ \n", " 2x_1 - 2x_2 + 7x_3 &= 17 \\\\\n", " -x_1 +2x_2 - 4x_3 &= -11 \\\\ \n", " \\end{aligned}$$\n", "\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Solution:**\n", "\n", "Running Gaussian Elimination\n", "\n", "\n", "Creating Echelon Form\n", "\n", " [[ 3 -3 9 24 ]\n", " [ 2 -2 7 17 ]\n", " [ -1 2 -4 -11 ]]\n", "\n", "R1 = (1/3)*R1\n", "\n", " [[ 1 -1 3 8 ]\n", " [ 2 -2 7 17 ]\n", " [ -1 2 -4 -11 ]]\n", "\n", "R2 = R2 - 2*R1\n", "\n", " [[ 1 -1 3 8 ]\n", " [ 0 0 1 1 ]\n", " [ -1 2 -4 -11 ]]\n", "\n", "R3 = R3 + R1\n", "\n", " [[ 1-1 3 8 ]\n", " [ 0 0 1 1 ]\n", " [ 0 1-1-3 ]]\n", "\n", "Exchange R3 and R2\n", "\n", " [[ 1-1 3 8 ]\n", " [ 0 1-1-3 ]\n", " [ 0 0 1 1 ]]\n", "\n", "Back Substituting\n", "\n", "Back substitute X3\n", "\n", "R2 = R2 + R3\n", "\n", " [[ 1-1 3 8 ]\n", " [ 0 1 0-2 ]\n", " [ 0 0 1 1 ]]\n", "\n", "R1 = R1 - 30*R3\n", "\n", " [[ 1-1 0 5 ]\n", " [ 0 1 0-2 ]\n", " [ 0 0 1 1 ]]\n", "\n", "Back substitute X2\n", "\n", "R1 = R1 + R2\n", "\n", " [[ 1 0 0 3 ]\n", " [ 0 1 0-2 ]\n", " [ 0 0 1 1 ]]\n", "\n", "Final Matrix:\n", "\n", " [[ 1 0 0 3 ]\n", " [ 0 1 0-2 ]\n", " [ 0 0 1 1 ]]\n", " \n", " \n", "The solution is thus:\n", "\n", "$$\\begin{aligned}\n", " x_1 &= 3 \\\\ \n", " x_2 &= -2 \\\\\n", " x_3 &= 1 \\\\ \n", " \\end{aligned}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Problem 8\n", "\n", " \n", " \n", "(B) Find the *parametric form* for the solution to the following set of equations by using the Gaussian Elimination algorithm by hand (the *general solution* is\n", "the listing of the values of each of the variables, in terms of the free variables, which are then parameters for an infinite set of solutions). \n", "\n", "Show all work, including the matrices produced after each row operation, and give the parametric form solution (hint: the variable $x_3$ will be free and hence a parameter). \n", "\n", "Again, you should have integers at each step, just to make the calculation easier by hand. \n", "\n", "\n", "$$\\begin{aligned}\n", " 3x_1 - 3x_2 + 3x_3 &= 9 \\\\ \n", " 2x_1 - x_2 + 4x_3 &= 7 \\\\\n", " 3x_1 - 5x_2 - x_3 &= 7 \\\\ \n", " \\end{aligned}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Solution:**\n", "\n", "Running Gaussian Elimination\n", "\n", "\n", "Creating Echelon Form\n", "\n", " [[ 3 -3 3 9 ]\n", " [ 2 -1 4 7 ]\n", " [ 3 -5 -1 7 ]]\n", "\n", "R1 = (1/3)* R1\n", "\n", " [[ 1 -1 1 3 ]\n", " [ 2 -1 4 7 ]\n", " [ 3 -5 -1 7 ]]\n", "\n", "R2 = R2 - 2*R1\n", "\n", " [[ 1 -1 1 3 ]\n", " [ 0 1 2 1 ]\n", " [ 3 -5 -1 7 ]]\n", "\n", "R3 = R3 - 3*R1\n", "\n", " [[ 1 -1 1 3 ]\n", " [ 0 1 2 1 ]\n", " [ 0 -2 -4 -2 ]]\n", "\n", "R3 = R3 + -2*R2\n", "\n", " [[ 1 -1 1 3 ]\n", " [ 0 1 2 1 ]\n", " [ 0 0 0 0 ]]\n", " \n", "Back substituting.....\n", "\n", "R1 = R1 + R2\n", "\n", " [[ 1 0 3 4 ]\n", " [ 0 1 2 1 ]\n", " [ 0 0 0 0 ]]\n", " \n", "The solution is thus:\n", "\n", "$$\\begin{aligned}\n", " x_1 &= -3x_3 + 4 \\\\ \n", " x_2 &= -2x_3 + 1 \\\\\n", " \\end{aligned}$$\n", "where $x_3$ is a parameter and can have any real value. \n" ] }, { "attachments": { "Screen%20Shot%202021-05-26%20at%2011.54.00%20PM.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "## Problem 9\n", "\n", "In this problem we are going to apply the elimination algorithm to solve a problem in \"curve fitting,\" that is,\n", "finding a quadratic equation of the form\n", "\n", "$$f(x) = a + bx + cx^2$$\n", "\n", "for some constants $a$, $b$, and $c$, which goes through the points $(1,-1)$, $(2,3)$, and $(3,13)$: \n", "\n", "![Screen%20Shot%202021-05-26%20at%2011.54.00%20PM.png](attachment:Screen%20Shot%202021-05-26%20at%2011.54.00%20PM.png)\n", "\n", "We can accomplish this useful task by\n", "construing the problem in terms of finding the unknowns $a$, $b$, and $c$ (hence, these are the variables, which\n", "we normally call $x_1$, $x_2$, and $x_3$). This technique, which involves treating the unknown\n", "constants as variables, is a fairly typical application of Gaussian Elimination. \n", "\n", "We will set up the problem using one equation for each of the points which the curve must fit, for example,\n", "the point $(2,3)$ must satisfy\n", "\n", "$$a + b\\cdot 2 + c\\cdot 2^2 = 3$$\n", "\n", "which, phrased as an equation in the three variables $a$, $b$, and $c$, is\n", "\n", "$$a + 2b + 4c = 3$$\n", "\n", "(A) Give the set of three equations in the variables $a$, $b$, and $c$ representing the problem to be solved. \n", "\n", "(B) Solve the problem by using Gaussian Elimination by hand, showing the matrix at each step, which will arrive\n", "at a unique solution. \n", "\n", "(C) Give the unique solution as a formula for $f(x)$ which fits the points. \n", "\n", "(D) Insert your values for $a$, $b$, and $c$ into the code fragment below to display the points and the curve. \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Solution:**\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Solution:** \n", "\n", "(A) The linear system is:\n", "\n", "$$\\begin{aligned}\n", " a + b + c &= -1 \\\\ \n", " a + 2b + 4c &= 3 \\\\\n", " a + 3b + 9c &= 13 \\\\ \n", " \\end{aligned}$$\n", " \n", "Running Gaussian Elimination...\n", "\n", "\n", "Creating Echelon Form...\n", "\n", " [[ 1. 1. 1. -1.]\n", " [ 1. 2. 4. 3.]\n", " [ 1. 3. 9. 13.]]\n", "\n", "R2 = R2 - R1\n", "\n", " [[ 1. 1. 1. -1.]\n", " [ 0. 1. 3. 4.]\n", " [ 1. 3. 9. 13.]]\n", "\n", "R3 = R3 - R1\n", "\n", " [[ 1. 1. 1. -1.]\n", " [ 0. 1. 3. 4.]\n", " [ 0. 2. 8. 14.]]\n", "\n", "R3 = R3 - 2.0*R2\n", "\n", " [[ 1. 1. 1. -1.]\n", " [ 0. 1. 3. 4.]\n", " [ 0. 0. 2. 6.]]\n", "\n", "R3 = 0.5*R3\n", "\n", " [[ 1. 1. 1. -1.]\n", " [ 0. 1. 3. 4.]\n", " [ 0. 0. 1. 3.]]\n", "\n", "Back Substituting....\n", "\n", "Back substitute X3\n", "\n", "R2 = R2 - 3.0*R3\n", "\n", " [[ 1. 1. 1. -1.]\n", " [ 0. 1. 0. -5.]\n", " [ 0. 0. 1. 3.]]\n", "\n", "R1 = R1 - R3\n", "\n", " [[ 1. 1. 0. -4.]\n", " [ 0. 1. 0. -5.]\n", " [ 0. 0. 1. 3.]]\n", "\n", "Back substitute X2\n", "\n", "R1 = R1 - R2\n", "\n", " [[ 1. 0. 0. 1.]\n", " [ 0. 1. 0. -5.]\n", " [ 0. 0. 1. 3.]]\n", "\n", "Final Matrix:\n", "\n", " [[ 1. 0. 0. 1.]\n", " [ 0. 1. 0. -5.]\n", " [ 0. 0. 1. 3.]]\n", " \n", "So the system is consistent and has a unique solution (good!)\n", "\n", "\n", "So the final solution is \n", "\n", "$$\\begin{aligned}\n", " a &= 1 \\\\ \n", " b &= -5 \\\\\n", " c &= 3 \\\\ \n", " \\end{aligned}$$\n", " \n", "and the polynomial is\n", "\n", "$$f(t) = 1 - 5t + 3t^2.$$\n", " \n", "as shown in the display in the next code cell. " ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Solution for (D): insert your values for a, b, and c here:\n", "\n", "a = 1 # replace with your values found above \n", "b = -5\n", "c = 3\n", "\n", "def f(t):\n", " return a + b*t + c*t*t\n", "\n", "\n", "plt.title('Curve Fitting Example')\n", "plt.xlabel(\"X\")\n", "plt.ylabel(\"Y\")\n", "X = np.linspace(0,3.5,100) \n", "Y = [f(x) for x in X]\n", "plt.plot(X,Y)\n", "plt.scatter([1,2,3], [-1,3,13])\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Problem 10\n", "\n", "In this problem, you must find the circle that runs through the points (5,5), (4,6), and (6,2). Write your equation in the form\n", "\n", "$$a+bx+cy+x^2+y^2 = 0.$$ \n", "\n", "(A) Give the original set of equations encoding this problem, the initial matrix, and the reduced row echelon form\n", "after running GE (do by hand, it s not that hard). \n", "\n", "(B) Calculate the center and radius of this circle;\n", "\n", "(C) Complete the code template below to display the circle, verifying that it runs through the points given. \n", "\n", "Hints: \n", "\n", "- The points are of the form (x,y) - plug each point into the equation to generate your system of linear equations with variables a, b, and c. \n", "\n", "- To find the center $(x_c,y_c)$ and radius $r$ of the resulting equation, rearrange it into the form \n", "\n", "$$(x-x_c)^2+(y- y_c)^2 = r^2.$$\n", "\n", "Here is a further explanation of how to do this rearrangement. \n", "\n", "\n", "First, find values for a, b, and c.   Then, you need to find values $x_c, y_c, r$ so you can transform\n", "\n", "the first equation into the second:\n", "\n", "\n", "\n", "\n", "$$a+bx+cy+x^2+y^2 = 0$$\n", "\n", "\n", "\n", "\n", "$$x^2 + bx + y^2 + cy = -a$$\n", "\n", "\n", "\n", "\n", "$$(x^2 + bx + x_c^2) + (y^2 + cy + y_c^2) = x_c^2 + y_c^2 - a$$\n", "\n", "\n", "\n", "\n", "$$(x - x_c)^2 + (y - y_c)^2 = r^2$$\n", "\n", "\n", "\n", "\n", "The last step consists in \"completing the squares\" to get the final equation (this process is discussed in\n", "the Math Review, or you can Google it!). \n", "\n", "Once you get the a, b, and c, this may be more obvious.  \n", "\n", "\n" ] }, { "attachments": { "Screen%20Shot%202021-07-08%20at%2011.23.21%20AM.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "**Solution:**\n", "\n", "![Screen%20Shot%202021-07-08%20at%2011.23.21%20AM.png](attachment:Screen%20Shot%202021-07-08%20at%2011.23.21%20AM.png)" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Solution for (C): \n", "\n", "x_c = 1 # put your solutions here\n", "y_c = 2\n", "r = 5\n", "\n", "# You shouldn't have to touch any of this code\n", "\n", "plt.figure(figsize=(10,10))\n", "plt.title('Solution (C)')\n", "plt.grid()\n", "plt.xlabel(\"X\")\n", "plt.ylabel(\"Y\")\n", "plt.xlim([-8,8])\n", "plt.ylim([-8,8])\n", "T = np.linspace(0,2*np.pi,100) # (cos(theta), sin(theta)) \n", "X = [r*np.cos(theta)+x_c for theta in T]\n", "Y = [r*np.sin(theta)+y_c for theta in T]\n", "plt.plot(X,Y)\n", "plt.plot([-8,8,0,0,0],[0,0,0,8,-8],color='k')\n", "plt.scatter([5,4,6], [5,6,2])\n", "plt.scatter([x_c], [y_c],marker='x')\n", "plt.show()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.6" } }, "nbformat": 4, "nbformat_minor": 2 }