0011.ptx

<exercise checkit-seed="0011" checkit-slug="M1" checkit-title="Multiplying matrices">
  <statement>
    <p>Of the following three matrices, only two may be multiplied.
      <me>
          A= \left[\begin{array}{cc}
1 &amp; -6 \\
0 &amp; 1 \\
1 &amp; -1 \\
0 &amp; -1
\end{array}\right]  \hspace{1em} B= \left[\begin{array}{ccc}
0 &amp; -2 &amp; -5 \\
-1 &amp; 6 &amp; 4 \\
0 &amp; -5 &amp; -4 \\
-1 &amp; 3 &amp; -2
\end{array}\right]  \hspace{1em} C= \left[\begin{array}{ccc}
0 &amp; -1 &amp; 1 \\
1 &amp; 3 &amp; -5
\end{array}\right] </me>
      Explain which two can be multiplied and why. Then show how to find their product.</p>
  </statement>
  <answer>
    <me>AC= \left[\begin{array}{ccc}
-6 &amp; -19 &amp; 31 \\
1 &amp; 3 &amp; -5 \\
-1 &amp; -4 &amp; 6 \\
-1 &amp; -3 &amp; 5
\end{array}\right] </me>
  </answer>
</exercise>