0011.tex

\begin{exercise}{M1}{Multiplying matrices}{0011}
\begin{exerciseStatement}

Of the following three matrices, only two may be multiplied. \[
          A= \left[\begin{array}{cc}
1 & -6 \\
0 & 1 \\
1 & -1 \\
0 & -1
\end{array}\right]  \hspace{1em} B= \left[\begin{array}{ccc}
0 & -2 & -5 \\
-1 & 6 & 4 \\
0 & -5 & -4 \\
-1 & 3 & -2
\end{array}\right]  \hspace{1em} C= \left[\begin{array}{ccc}
0 & -1 & 1 \\
1 & 3 & -5
\end{array}\right] \] Explain which two can be multiplied and why. Then show how to find their product.

\end{exerciseStatement}
\begin{exerciseAnswer}\[AC= \left[\begin{array}{ccc}
-6 & -19 & 31 \\
1 & 3 & -5 \\
-1 & -4 & 6 \\
-1 & -3 & 5
\end{array}\right] \]\end{exerciseAnswer}
\end{exercise}