{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Assignment 2 " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# MATH 7502 - Semsester 2, 2018\n", "## Mathematics for Data Science 1\n", "\n", "#### Created by Zhihao Qiao, Maria Kleshnina and Yoni Nazarathy" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Question 1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "(a) Find the general solutions of the system whose augmented matrix is given by \n", "$$ \\begin{bmatrix}\n", "1&-7&0&6&5\\\\\n", "0&0&1&-2&-3\\\\\n", "-1&7&-4&2&7\n", "\\end{bmatrix}.$$\n", "(b) Under what condition on $b_1,b_2,b_3$ is this system solvable? \n", "$$ \\begin{align*}\n", "&x+2y-2z=b_1\\\\\n", "&2x+5y-4z=b_2\\\\\n", "&4x+9y-8z=b_3.\n", "\\end{align*}$$\n", "\n", "(c) Give an exmaple of an incosistent undetermined system of two equations with three unknowns. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Question 2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "(a) Let $v_1 = \\begin{bmatrix}\n", "1\\\\\n", "0\\\\\n", "-2\n", "\\end{bmatrix}, v_2= \\begin{bmatrix}\n", "-3\\\\\n", "1\\\\\n", "8\n", "\\end{bmatrix},$ and $y = \\begin{bmatrix}\n", "h\\\\\n", "-5\\\\\n", "-3\n", "\\end{bmatrix}$. For what value(s) of h is y in the plane spanned by $v_1$ and $v_2$. \n", "\n", "(b) Explain why $\\{ \\begin{bmatrix}\n", "1\\\\\n", "-1\n", "\\end{bmatrix},\n", "\\begin{bmatrix}\n", "1\\\\\n", "2\n", "\\end{bmatrix} \\}$ is a basis for $R^2$ (Hint: Write $e_1$ and $e_2$ as linear combinations of these vectors.)\n", "\n", "(c) Find three different bases for the column space of $U = \\begin{bmatrix}\n", "1&0&1&0&1\\\\\n", "0&1&0&1&0\n", "\\end{bmatrix}.$ Then find two different bases for the row space of $U$. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Question 3 " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Consider the transofrmation $T: R^3 \\rightarrow R^3$ that projects vectors onto the line $ l = \\begin{bmatrix}\n", "0\\\\\n", "0\\\\\n", "0\n", "\\end{bmatrix}+ t\n", "\\begin{bmatrix}\n", "1\\\\\n", "0\\\\\n", "1\n", "\\end{bmatrix}. t \\in R$\n", "\n", "(a) Find a formula for $T\\bigg(\\begin{bmatrix}\n", "x\\\\\n", "y\\\\\n", "z\n", "\\end{bmatrix}\\bigg)$, and prove that T is a linear transformation. \n", "\n", "(b) Find matrix A, asssociated with T. \n", "\n", "(c) Determine the relationship between the row space of A row(A) and the line $l$. \n", "\n", "(d) Determine the null space, Null(A). " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Question 4" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "(a) Define $A = \\begin{bmatrix}\n", "0&1\\\\\n", "2&1\n", "\\end{bmatrix}$, Find the eigenvalues and associated eigenvectors of A.\n", "\n", "(b) Can you represent $\\begin{bmatrix}\n", "8\\\\\n", "10\n", "\\end{bmatrix}$ as a linear combination of the eigenvectors? If so , do so. \n", "\n", "(c) Consider the linear transformation $ T: R^2 \\rightarrow R^2$ where $T(v) = Av$. Suppose $n$ is a postive integer and we write $T^n:R^2 \\rightarrow R^2$ for the composition of $T$ with itself $n$ times. Use your answer in (a) and (b) to calculate \n", "$$ T^{47} \\bigg(\\begin{bmatrix}\n", "8\\\\\n", "10\n", "\\end{bmatrix}\\bigg) $$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Question 5" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " Suppose we have matrices $A, B, X, $ and $Y$ with $AX=BY$. \n", "\n", "(a) Give an example showing that $A\\neq 0$ is not enough to conclude that $X=Y$. \n", "\n", "(b) Show that if $A$ is left-invertible, we can conlcude from $AX=AY$ that $X=Y$.\n", "\n", "(c) Show that if $A$ is not left-invertible, there are matrices $X$ and $Y$ with $X \\neq Y$, and $AX=AY$. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Question 6" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Consider the stacked vectors \n", "$$ c_1 = \\begin{bmatrix}\n", "a_1\\\\\n", "b_1\n", "\\end{bmatrix}, . . . . . c_k = \\begin{bmatrix}\n", "a_k\\\\\n", "b_k\n", "\\end{bmatrix}.$$\n", "\n", "where $a_1,...,a_k$ are n-vectors and $b_1,...,b_k$ are m-vectors. For each case, either prove or provide a counter example. \n", "\n", "(a) Suppose $a_1,...,a_k$ are linearly independent (we make no assumptions about $b_1,...,b_k$). Can we conclude that the stacked vectors $c_1,...,c_k$ are linearly indepndent?\n", "\n", "(b) Suppose $a_1,...,a_k$ are linearly dependent (we make no assumptions about $b_1,...,b_k$). Can we conclude that the stacked vectors $c_1,...,c_k$ are linearly depndent?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Question 7" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let $G \\in R^{m\\times n}$ represent a contignecy matrix of $m$ students who are members of $n$ groups with\n", "\n", "\\begin{equation*}\n", "G_{ij} = \\begin{cases}\n", "1 &\\text{ student i is in group j }\\\\\n", "0 &\\text{ student i is not in group j}\n", "\\end{cases}\n", "\\end{equation*}\n", "\n", "(a) What is the meaning of the 3rd column of $G$?\n", "\n", "(b) What is the meaning of the 2nd row of $G$?\n", "\n", "(c) Give a simple formula for the n-vectors $M$, where $M_i$ is the total membership in the group $i$. \n", "\n", "(d) Interpret $(GG^T)_{ij}$ in simple Enlgish.\n", "\n", "(e) Interpret $(G^T G)_{ij}$ in simple English. \n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Question 8" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "An n-vector $x$ is symmetric if $x_k = x_{n-k+1}$ for $k=1,...,n.$ It is anti-symmetric if $x_k = -x_{n-k+1}$ for $k=1,...n.$\n", "\n", "(a) Show that every vector $x$ can be decomposed in a unique way as sum $x=x_s+x_a$ of a symmetric vector $x_s$ and an anti-symmetric vector $x_a$.\n", "\n", "(b) Show that the symmetric and anti-symmetric parts $x_s$ and $x_a$ are linear functions of $x$. Given matrices $A_s$ and $A_a$ such that $x_s = A_s x$, and $x_a = A_a x$ for all $x$. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Question 9" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For descriptions of $y$ below, express it as $y=Ax$ for some $A$ (You should specify $A$). \n", "\n", "(a) $y_i$ is the difference between $x_i$ and the average of $x_1,...,x_{i-1}.$ (We take $y_1=x_1$). \n", "\n", "(b) $y_i$ is the difference between $x_i$ and the average value of all other $x_j$. i.ie the average of $x_1,...,x_{i-1}, x_{i+1},...,x_n$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Question 10 \n", "Write your own code to implement the Grah-Schmidt procedure. Test your code and find an orthogonal basis of \n", "\n", "\n", "$$ \\bigg\\{\\begin{bmatrix}\n", "1\\\\\n", "2\\\\\n", "3\\\\\n", "0\\\\\n", "\\end{bmatrix}, \n", "\\begin{bmatrix}\n", "1\\\\\n", "2\\\\\n", "0\\\\\n", "0\\end{bmatrix},\n", "\\begin{bmatrix}\n", "1\\\\\n", "0\\\\\n", "0\\\\\n", "1\\end{bmatrix}\\bigg\\}.$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Question 11 \n", "The following code geneartes a signal together with noise.\n", "\n", "(a) Compute and plot the fourier transform of the signal without noise.\n", "\n", "(b) Compute and plot the the fourier transform with signal noise. \n", "\n", "(c) Corruput the signal with different white-noise, and reproduce the plot of (a) and (b)." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "PyPlot.Figure(PyObject
)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "using PyPlot\n", "\n", "Fs = 1000; #Sampling frequency \n", "T = 1/Fs; #Sampling period \n", "L = 1500; #Length of signal\n", "t = (0:L-1)*T; #Time vector\n", "\n", "#Form a signal containing a 25 Hz sinusoid of amplitude 0.9 and a 120 Hz sinusoid of amplitude 1.\n", "S = 0.9*sin.(2*pi*25*t) + sin.(2*pi*120*t);\n", "#Corrupt the signal with zero-mean white noise with a variance of 4.\n", "X = S+2*randn(size(t));\n", "\n", "plot(1000*t[1:50],X[1:50])\n", "title(\"Signal Corrupted with Zero-Mean Random Noise\")\n", "xlabel(\"t (milliseconds)\")\n", "ylabel(\"X(t)\");" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "PyPlot.Figure(PyObject
)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "## Compute the FFT for the term without noise \n", "Z=abs(fft(S))\n", "## frequency axis\n", "f = Fs*(0:(L-1))/L;\n", "plot(f,Z)\n", "xlabel(\"f (Hz)\")\n", "ylabel(\"|S(f)|\");" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "PyPlot.Figure(PyObject
)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "## Compute the FFT for the term without noise \n", "Y=abs(fft(X))\n", "## frequency axis\n", "f = Fs*(0:(L-1))/L;\n", "plot(f,Y)\n", "xlabel(\"f (Hz)\")\n", "ylabel(\"|Y(f)|\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Question 12\n", "\n", "Explain the results of the previous question. How can Fourier analysis be used in data science? Present a 1-2 paragraph subjective description." ] } ], "metadata": { "kernelspec": { "display_name": "Julia 0.6.2", "language": "julia", "name": "julia-0.6" }, "language_info": { "file_extension": ".jl", "mimetype": "application/julia", "name": "julia", "version": "0.6.2" } }, "nbformat": 4, "nbformat_minor": 2 }