CE_Mar21.tex

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\begin{document}
\begin{center}
\Large
\rm{Math 221}
\\
\rm{Class Exercises:  Mar. 21}
\\
\end{center}
\vspace{0.2in}
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Let $U=\left\{\left[ \begin{array}{ccc} x & y & z   \end{array}\right]^T: x+3z=0\right\}$

\begin{enumerate}
	\item {Find a basis for $U$.}
	\item {Find an orthonormal basis for $U$.}
	\item {Find a basis for $U^{\perp}$.}
	\item {Find $\Proj_U(v)$ where
	\begin{displaymath}
	v = \left[ \begin{array}{r} 1 \\ 1 \\ -1   \end{array}\right]
	\end{displaymath}}
\end{enumerate}



\end{document}