CE_Apr4.tex

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\begin{document}

\begin{center}
	\Large
	\rm{Math 221}
	\\
	\rm{Class Exercises:  Apr. 4}
	\\
\end{center}
\vspace{0.2in}
\fboxsep0.5cm

\begin{enumerate}
\item{Fill in the second row of the matrix $A$ so that it has eigenvalues 1, and 5.
	\begin{displaymath}
	A = \left[ \begin{array}{rr} 0&1 \\
	* & *  \end{array} \right]
	\end{displaymath}
	}

\vspace{0.5in}

\item{Suppose $B=QDQ^{-1}$ where

\begin{displaymath}
Q = \left[ \begin{array}{c|c|c} & &  \\ u & v & w \\ & &   \end{array} \right] \quad\quad
D = \left[ \begin{array}{ccc}  0 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 5  \end{array} \right] 
\end{displaymath}	

\begin{enumerate}
	\item {Give a basis for $\mathcal{N}(A)$.}
	\item {Find all solutions of $Ax=v+w$.}
\end{enumerate}
}

\end{enumerate}

\vspace{0.1in}
\end{document}