206 lines
7.8 KiB
TeX
206 lines
7.8 KiB
TeX
\documentclass[addpoints,10pt]{exam}
|
|
\usepackage{url}
|
|
\usepackage{color}
|
|
\usepackage{hyperref}
|
|
\usepackage{graphicx}
|
|
\usepackage{amsmath}
|
|
|
|
\pagestyle{headandfoot}
|
|
\runningheadrule
|
|
\firstpageheadrule
|
|
|
|
\firstpageheader{Scientific Computing}{Matrix multiplication}{Oct 28, 2014}
|
|
%\runningheader{Homework 01}{Page \thepage\ of \numpages}{23. October 2014}
|
|
\firstpagefooter{}{}{}
|
|
\runningfooter{}{}{}
|
|
\pointsinmargin
|
|
\bracketedpoints
|
|
|
|
%\printanswers
|
|
\shadedsolutions
|
|
|
|
\usepackage[mediumspace,mediumqspace,Gray]{SIunits} % \ohm, \micro
|
|
|
|
%%%%% listings %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
\usepackage{listings}
|
|
\lstset{
|
|
basicstyle=\ttfamily,
|
|
numbers=left,
|
|
showstringspaces=false,
|
|
language=Matlab,
|
|
breaklines=true,
|
|
breakautoindent=true,
|
|
columns=flexible,
|
|
frame=single,
|
|
captionpos=t,
|
|
xleftmargin=2em,
|
|
xrightmargin=1em,
|
|
aboveskip=10pt,
|
|
%title=\lstname,
|
|
title={\protect\filename@parse{\lstname}\protect\filename@base.\protect\filename@ext}
|
|
}
|
|
|
|
|
|
\begin{document}
|
|
|
|
\sffamily
|
|
%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
|
\begin{questions}
|
|
\question \textbf{Matrix multiplication}
|
|
Calculate the results of the following matrix multiplications and
|
|
confirm the result using matlab.
|
|
\[ \begin{pmatrix} 2 \\ -4 \\ -1 \end{pmatrix} \cdot
|
|
\begin{pmatrix} 3 & -4 & -4 \end{pmatrix} = \]
|
|
|
|
\[ \begin{pmatrix} 3 & -3 & -1 \end{pmatrix} \cdot
|
|
\begin{pmatrix} 2 \\ 3 \\ 0 \end{pmatrix} = \]
|
|
|
|
\[ \begin{pmatrix} 4 & -1 & 2 \\ -1 & 3 & 1 \\ 4 & -2 & 1 \\ 4 & -3 & -2 \end{pmatrix} \cdot
|
|
\begin{pmatrix} -2 & -2 & 0 & -3 \\ 3 & -2 & 1 & 0 \\ 1 & -2 & -4 & 0 \end{pmatrix} = \]
|
|
|
|
\[ \begin{pmatrix} 3 & 1 \\ 1 & 4 \end{pmatrix} \cdot
|
|
\begin{pmatrix} 0 & -3 & 4 & 1 \\ -2 & -1 & -2 & -3 \\ -3 & 1 & -2 & -3 \end{pmatrix} = \]
|
|
|
|
\[ \begin{pmatrix} 1 & 1 & -4 \end{pmatrix} \cdot
|
|
\begin{pmatrix} -1 \\ 2 \end{pmatrix} = \]
|
|
|
|
\[ \begin{pmatrix} 3 & 1 & -2 \\ 2 & 1 & 3 \\ 1 & 1 & 2 \end{pmatrix} \cdot
|
|
\begin{pmatrix} 2 & 2 \\ -3 & 3 \\ -4 & 1 \end{pmatrix} = \]
|
|
|
|
\[ \begin{pmatrix} 3 \\ 2 \end{pmatrix} \cdot
|
|
\begin{pmatrix} -3 & 2 & -4 & 1 \end{pmatrix} = \]
|
|
|
|
\[ \begin{pmatrix} -1 \\ -4 \\ -1 \end{pmatrix} \cdot
|
|
\begin{pmatrix} 0 & -4 & 1 \end{pmatrix} = \]
|
|
|
|
\[ \begin{pmatrix} 4 & -2 & -2 & -4 \end{pmatrix} \cdot
|
|
\begin{pmatrix} 2 \\ 2 \\ 1 \\ -1 \end{pmatrix} = \]
|
|
|
|
\[ \begin{pmatrix} -2 & -3 & -4 \\ 1 & 3 & 2 \\ -4 & -2 & 1 \end{pmatrix} \cdot
|
|
\begin{pmatrix} 1 & 2 & -2 & 4 \\ 3 & -1 & 1 & -1 \\ -3 & 2 & -1 & 2 \end{pmatrix} = \]
|
|
|
|
\[ \begin{pmatrix} 2 & -4 & 4 & 4 \\ -3 & 3 & 2 & 1 \end{pmatrix} \cdot
|
|
\begin{pmatrix} 0 & 3 & 4 & -2 \\ -4 & -2 & -1 & 0 \\ 1 & 2 & -4 & -4 \\ 3 & 2 & -2 & -4 \end{pmatrix} = \]
|
|
|
|
\[ \begin{pmatrix} 3 & 1 & -2 & -2 \end{pmatrix} \cdot
|
|
\begin{pmatrix} -4 \\ 3 \\ -2 \\ 4 \end{pmatrix} = \]
|
|
|
|
\[ \begin{pmatrix} -1 & 3 & 4 \end{pmatrix} \cdot
|
|
\begin{pmatrix} -1 \\ 4 \\ -3 \end{pmatrix} = \]
|
|
|
|
\[ \begin{pmatrix} 1 & -4 & 3 & 3 \end{pmatrix} \cdot
|
|
\begin{pmatrix} 1 \\ 0 \\ -4 \\ -1 \end{pmatrix} = \]
|
|
|
|
\[ \begin{pmatrix} -4 & -4 & -3 \\ -2 & -2 & 4 \\ -3 & 4 & -3 \end{pmatrix} \cdot
|
|
\begin{pmatrix} 0 & 3 & -4 & 4 \\ -1 & -2 & -3 & 1 \\ 1 & -2 & 2 & 0 \end{pmatrix} = \]
|
|
|
|
\[ \begin{pmatrix} -3 & 0 & 4 & 1 \\ 0 & 1 & 1 & 4 \end{pmatrix} \cdot
|
|
\begin{pmatrix} -4 & 3 & 1 & 4 \\ 1 & -4 & 1 & -3 \\ -4 & 0 & -4 & -4 \\ 1 & -2 & 4 & 4 \end{pmatrix} = \]
|
|
|
|
\[ \begin{pmatrix} 4 \\ 3 \\ 4 \\ -2 \end{pmatrix} \cdot
|
|
\begin{pmatrix} 2 & 4 & 3 & 3 \end{pmatrix} = \]
|
|
|
|
\[ \begin{pmatrix} 1 & 2 & 0 & 3 \end{pmatrix} \cdot
|
|
\begin{pmatrix} -3 \\ 1 \\ 1 \end{pmatrix} = \]
|
|
|
|
\[ \begin{pmatrix} -4 & 0 & -1 & 3 \\ 0 & -4 & 3 & -3 \end{pmatrix} \cdot
|
|
\begin{pmatrix} -1 & -4 & -1 \\ 3 & 2 & 0 \\ -2 & 3 & -2 \\ 1 & 2 & -2 \end{pmatrix} = \]
|
|
|
|
\[ \begin{pmatrix} 2 & 0 & 3 \\ 1 & -4 & -1 \\ 3 & 0 & -2 \end{pmatrix} \cdot
|
|
\begin{pmatrix} 0 & 2 & -1 & -2 \\ -1 & -1 & -3 & 4 \\ 2 & 4 & -4 & 1 \end{pmatrix} = \]
|
|
\[ \begin{pmatrix} -1 & 4 \end{pmatrix} \cdot
|
|
\begin{pmatrix} 0 \\ 1 \end{pmatrix} = \]
|
|
|
|
\[ \begin{pmatrix} -4 & 3 \\ -4 & 0 \\ -2 & -2 \end{pmatrix} \cdot
|
|
\begin{pmatrix} 0 & 1 & -4 & 2 \\ 2 & 3 & -2 & -1 \end{pmatrix} = \]
|
|
|
|
\[ \begin{pmatrix} -2 & -1 \end{pmatrix} \cdot
|
|
\begin{pmatrix} 1 \\ -2 \end{pmatrix} = \]
|
|
|
|
\[ \begin{pmatrix} -2 & 2 & -2 & -3 \\ 2 & -4 & -2 & 2 \\ 0 & 2 & -2 & -2 \\ 1 & -2 & -2 & -2 \end{pmatrix} \cdot
|
|
\begin{pmatrix} 1 & -2 & 2 \\ -4 & -2 & -2 \\ 3 & 1 & 4 \\ -4 & 1 & -2 \end{pmatrix} = \]
|
|
|
|
\[ \begin{pmatrix} -1 & -3 & 0 & -1 \\ 4 & -2 & 1 & 2 \end{pmatrix} \cdot
|
|
\begin{pmatrix} -3 & -4 \\ -4 & 0 \end{pmatrix} = \]
|
|
|
|
\[ \begin{pmatrix} -1 & 1 & -2 \\ -2 & 2 & -4 \\ 1 & -2 & -2 \end{pmatrix} \cdot
|
|
\begin{pmatrix} -1 & 2 & -4 \\ 1 & 3 & 0 \\ 1 & 4 & -4 \end{pmatrix} = \]
|
|
|
|
\[ \begin{pmatrix} -3 & 3 \\ -3 & 2 \end{pmatrix} \cdot
|
|
\begin{pmatrix} 2 & -3 \\ -2 & -4 \end{pmatrix} = \]
|
|
|
|
\[ \begin{pmatrix} 1 & 1 & -3 \end{pmatrix} \cdot
|
|
\begin{pmatrix} -1 \\ -2 \\ 3 \end{pmatrix} = \]
|
|
|
|
\[ \begin{pmatrix} -4 & 2 & 1 \\ 4 & 0 & -2 \\ 2 & 3 & -3 \\ -2 & -2 & -2 \end{pmatrix} \cdot
|
|
\begin{pmatrix} -1 & 2 & 0 & -2 \\ 2 & -2 & 0 & -1 \\ -4 & 3 & -3 & 4 \end{pmatrix} = \]
|
|
|
|
\[ \begin{pmatrix} -2 & -4 & 2 & 4 \\ 3 & -3 & 2 & 1 \end{pmatrix} \cdot
|
|
\begin{pmatrix} 0 & 4 & -1 & -4 \\ 2 & 3 & -4 & -1 \\ 3 & 2 & -2 & 4 \end{pmatrix} = \]
|
|
|
|
\[ \begin{pmatrix} -3 & -2 & -1 & -3 \end{pmatrix} \cdot
|
|
\begin{pmatrix} 2 \\ -2 \\ 3 \\ -2 \end{pmatrix} = \]
|
|
|
|
\[ \begin{pmatrix} 4 & 4 & 2 & 3 \end{pmatrix} \cdot
|
|
\begin{pmatrix} 3 \\ 3 \\ -2 \\ 1 \end{pmatrix} = \]
|
|
|
|
\[ \begin{pmatrix} 3 & 2 & -2 \end{pmatrix} \cdot
|
|
\begin{pmatrix} 2 \\ 4 \\ 3 \end{pmatrix} = \]
|
|
|
|
\[ \begin{pmatrix} 2 & -1 & 0 & -2 \\ 0 & -4 & -3 & -1 \end{pmatrix} \cdot
|
|
\begin{pmatrix} 4 & -3 & 2 & 4 \\ -3 & -4 & 1 & 1 \\ 1 & 3 & -2 & 3 \\ -1 & -2 & 3 & 0 \end{pmatrix} = \]
|
|
|
|
\[ \begin{pmatrix} -3 & -3 & 3 & 2 \\ 2 & 2 & -3 & 1 \end{pmatrix} \cdot
|
|
\begin{pmatrix} 0 & 1 \\ 4 & 2 \\ -3 & -1 \\ -3 & 4 \end{pmatrix} = \]
|
|
|
|
\[ \begin{pmatrix} -4 & -3 \end{pmatrix} \cdot
|
|
\begin{pmatrix} -2 \\ 3 \\ 4 \end{pmatrix} = \]
|
|
|
|
\[ \begin{pmatrix} 4 & 4 \end{pmatrix} \cdot
|
|
\begin{pmatrix} 1 \\ 4 \\ -1 \end{pmatrix} = \]
|
|
|
|
\[ \begin{pmatrix} 1 & -2 & 3 \end{pmatrix} \cdot
|
|
\begin{pmatrix} 3 \\ 1 \\ 2 \end{pmatrix} = \]
|
|
|
|
\[ \begin{pmatrix} -3 & 2 \end{pmatrix} \cdot
|
|
\begin{pmatrix} -1 \\ 1 \end{pmatrix} = \]
|
|
|
|
\[ \begin{pmatrix} -2 & -4 & -4 & 0 \\ 0 & 3 & 4 & -4 \\ 4 & 2 & -2 & -4 \\ 0 & 0 & 4 & -1 \end{pmatrix} \cdot
|
|
\begin{pmatrix} 0 & -1 \\ -1 & 1 \\ -4 & -3 \\ 2 & 1 \end{pmatrix} = \]
|
|
|
|
\[ \begin{pmatrix} -3 \\ 3 \\ -3 \\ -4 \end{pmatrix} \cdot
|
|
\begin{pmatrix} 2 & 4 & -2 & 1 \end{pmatrix} = \]
|
|
|
|
\[ \begin{pmatrix} 2 \\ 0 \end{pmatrix} \cdot
|
|
\begin{pmatrix} -1 & -3 & -2 & 2 \end{pmatrix} = \]
|
|
|
|
\[ \begin{pmatrix} 0 & -4 & -4 & 4 \end{pmatrix} \cdot
|
|
\begin{pmatrix} 1 \\ 4 \\ 0 \\ 4 \end{pmatrix} = \]
|
|
|
|
\[ \begin{pmatrix} -3 & -1 \\ -3 & -1 \end{pmatrix} \cdot
|
|
\begin{pmatrix} 0 & -3 & 3 & -2 \\ -4 & 1 & -1 & 4 \end{pmatrix} = \]
|
|
|
|
\[ \begin{pmatrix} 4 & 0 \\ -1 & 4 \\ 1 & -3 \end{pmatrix} \cdot
|
|
\begin{pmatrix} -4 & -4 \\ -4 & 2 \end{pmatrix} = \]
|
|
|
|
\[ \begin{pmatrix} -1 \\ 3 \\ 2 \\ 4 \end{pmatrix} \cdot
|
|
\begin{pmatrix} 0 & -1 & 0 & 0 \end{pmatrix} = \]
|
|
|
|
\[ \begin{pmatrix} 3 \\ -2 \\ 2 \\ 3 \end{pmatrix} \cdot
|
|
\begin{pmatrix} -2 & -3 & -4 & 2 \end{pmatrix} = \]
|
|
|
|
\[ \begin{pmatrix} 2 & -2 & -4 & 4 \\ 0 & 1 & -3 & -2 \\ -1 & 3 & 0 & -2 \end{pmatrix} \cdot
|
|
\begin{pmatrix} -4 & 1 \\ -4 & 3 \end{pmatrix} = \]
|
|
|
|
\[ \begin{pmatrix} -4 & -1 & 3 \end{pmatrix} \cdot
|
|
\begin{pmatrix} -4 \\ -3 \\ 3 \end{pmatrix} = \]
|
|
|
|
\question \textbf{Automatic generation of exercises}
|
|
Write some matlab code that generates exercises like this one automatically! :-)
|
|
|
|
\end{questions}
|
|
|
|
|
|
\end{document}
|