\documentclass[12pt]{article}
\usepackage{latexsym}
%\input psfig.sty
\input spec_frac
\begin{document}
\title{314 '07-QUIZ 6}
\author{Name:\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ }
\maketitle
\section{$<15pts>$}
Compute $e^{A}$ if $A$ is the matrix
\[ A = 
\left[
\begin{array}{rr}
3 & 4 \\
\ -2  & \ -3
\end{array}
\right]
\]
{\bf Solution}\\

\newpage

\section{$<15pts>$}
Solve the initial value problem:
\begin{eqnarray*}
y_1^\prime & = & -2y_1 -4y_2  \ ,\  y_1(0) = 2\\
y_2^\prime & = & \ \ \ \ y_1 +3y_2\ ,\  y_2(0) = 1
\end{eqnarray*}

{\bf Solution}\\

\newpage

\section{$< 10pts >$}
Given the matrices $A$, $B$:
\[ A = \left[ 
\begin{array}{rrr}
-1 & 2 \\ 2 & 2
\end{array}
\right] \ ,\  
B = \left[ 
\begin{array}{rrr}
-1 & 0 \\ 0 & 2
\end{array}
\right]
\]
Is there a nonsingular matrix $S$ such that
\[ S^{-1} A S = B \ ? \]
If so find it. If not, explain why not.\\
{\bf Solution}\\

\end{document}
