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\begin{document}

\begin{center}
{\Large{\color{red}Homework 6}}

{\it Due Wednesday, April 25, 2007, at 11:00 am in class}

\end{center}


{\bf Remark:} I may not grade all assignments and may not grade all questions/parts on the 
assignment I grade.

\begin{enumerate}


\item Let 

\[
A= \left[
\begin{array}{ccc}
4 & 0 & 5  \\
3 & 2 & 1 \\
6 & 8 & 7
\end{array}
\right].\]

Find

\begin{enumerate}
\item $A^2 - 2 A^T$.
\item $\det(A)$ by using cofactors (the method we covered in class).
\item $A^{-1}$ by using the adjoint method.
\end{enumerate}


\item Solve the following system by using the inverse of the matrix in the previous question:


\begin{center}
$4x_1 + 5 x_3 = -1.$

$3x_1 + 2 x_2 + x_3 = -2.$

$6x_1 +  8 x_2 + 7 x_3 = -3.$
\end{center}

\end{enumerate}

\end{document}

