\documentclass[12pt]{amsart}

\title{Math 365: Honors Analysis I\\
Linear Systems Exercises}
\date{November 29, 2000}

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\newcommand{\X}{\mathbf{X}}
\renewcommand{\matrix}[4]{\left(\begin{array}{cc}#1&#2\\#3&#4\end{array}\right)}
\renewcommand{\vector}[2]{\left(\begin{array}{c}#1\\#2\end{array}\right)}

\begin{document}

\maketitle

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Find the general solution to the given system of equations.
\bigskip

\begin{enumerate}

\setlength{\itemsep}{15pt}

\item  $\X' = \matrix{3}{-2}{2}{-2}\X$

\item  $\X' = \matrix{-2}{1}{1}{-2}\X$

\item  $\X' = \matrix{2}{-5}{1}{-2}\X$

\item  $\X' = \matrix{3}{-2}{4}{-1}\X$

\item  $\X' = \matrix{4}{-2}{8}{-4}\X$

\item  $\X' = \matrix{1}{-4}{4}{-7}\X$

\item  $\X' = \matrix{1}{\sqrt{3}}{\sqrt{3}}{-1}\X +
\vector{e^t}{\sqrt{3}e^{-t}}$

\item  $\X' = \matrix{2}{-5}{1}{-2}\X +
\vector{-\cos(t)}{\sin(t)}$


\end{enumerate}

\end{document}
