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{\large Extra Credit 3 - 6 points}

This is due at the beginning of class, Monday, May 13.  \underline{Staple} extra sheets if needed to this sheet.
\begin{enumerate}

\item (1 point)  If the following matrix came from a system of equations, what were the equations?  Solve the system of equations.

\[
\left[ \begin{array}{rrrr|r}
2 & 5 & 0 & 1 & 11 \\
1 & 4 & 2 & -2 & -7 \\
2 & -2 & 5 & 1 & 3 \\
1 & 0 & 0 & -3 & 1 \\
\end{array} \right]
\]

\item (1 point)  Find $AB$ and $BA$ if possible.  If not possible, say so.
\[A = \left[ \begin{array}{rrrr}
2 & 1 \\
-3 & 4 \\
1 & 6 \\
\end{array} \right]
\]
\[
B = \left[ \begin{array}{rrrr}
0 & -1 & 0 \\
4 & 0 & 2 \\
8 & -1 & 7 \\ 
\end{array} \right]
\]

\item  (1 point)  Find the determinant:
\[
\begin{array}{|rrrr|}
2 & 5 & 0 & 1 \\
1 & 4 & 2 & -2 \\
2 & -2 & 5 & 1 \\
1 & 0 & 0 & -3 \\
\end{array} 
\]

\item (1 point)  Find the area of a triangle with vertices at $(-2,1),(3,-1),(1,6)$

\item (2 points)  Decode the message:

7 -21 -71 12 10 -11 5 -10 -40 53 80 54

The matrix used to encode the message was:
\[
A = \left[
\begin{array}{rrr}
1 & 2 & 2 \\
3 & 7 & 9 \\
-1 & -4 & -7 \\
\end{array}
\right]
\]

\end{enumerate}

\end{document}






