0004.tex

\begin{exercise}{M1}{Multiplying matrices}{0004}
\begin{exerciseStatement}

Of the following three matrices, only two may be multiplied. \[
          A= \left[\begin{array}{ccc}
2 & -1 & -1 \\
1 & 0 & -2 \\
3 & -1 & -2 \\
2 & -1 & -1
\end{array}\right]  \hspace{1em} B= \left[\begin{array}{cc}
3 & 3 \\
0 & 1 \\
-2 & -2 \\
1 & 0
\end{array}\right]  \hspace{1em} C= \left[\begin{array}{ccc}
3 & 5 & -3 \\
1 & 2 & -1
\end{array}\right] \] Explain which two can be multiplied and why. Then show how to find their product.

\end{exerciseStatement}
\begin{exerciseAnswer}\[BC= \left[\begin{array}{ccc}
12 & 21 & -12 \\
1 & 2 & -1 \\
-8 & -14 & 8 \\
3 & 5 & -3
\end{array}\right] \]\end{exerciseAnswer}
\end{exercise}