quiz1.tex

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\rm{Math 221-AB1:  Quiz 1}
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\begin{enumerate}
\item{(\emph{3 pts}) Determine the elementary matrix $E$ such that $EB$ has a zero in the third row, second column. 
	\begin{displaymath}
	B = \left[ \begin{array}{rrr} 2 &  6 & 4 \\ 4 & -1 & 3 \\ -1 & 3 & 1 \end{array} \right] \quad
	\end{displaymath}
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\item{(\emph{3 pts}) Suppose we know that 
\begin{displaymath}
C^{-1} = \left[ \begin{array}{rrr} 1 &  1 & 2 \\ 0 & k & 1 \\ 4 & 2 & -1 \end{array} \right] \quad
\end{displaymath}
\begin{enumerate}
\item{Find a matrix $D$ so that $CD= \left[ \begin{array}{rr} 1 &  1 \\ 0 &  1 \\  2 & -1 \end{array} \right] $.}
%\item{Find a matrix ${\bf C}$ so that ${\bf AC}= {\bf A}^2 + {\bf A}$.}
\end{enumerate}

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\item{(\emph{4 pts}) Solve the linear system $Ax=b$ with $A=LU$ where $L$, $U$, and $b$ given as 
\begin{displaymath}
L = \left[ \begin{array}{rr} 1 &  0 \\ 2 & 1 \end{array} \right] \quad 
U = \left[ \begin{array}{rrr} 2 &  -1 & 1 \\ 0 & 0 & 3 \end{array} \right] \quad 
b = \left[ \begin{array}{r} 1  \\ 8 \end{array} \right]
\end{displaymath}
Do not reconstruct $A$  and perform elimination. Make use of the factorization.
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\end{enumerate}

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