0011.ptx

<exercise checkit-seed="0011" checkit-slug="M2" checkit-title="Row operations as matrix multiplication">
  <statement>
    <p>Let <m>A</m> be a <m>4 \times 4</m> matrix.</p>
    <ol>
      <li>Give a <m>4 \times 4</m> matrix <m>B</m> that may be used to perform the row operation <m> R_4 \to R_4 + 3R_2 </m>.</li>
      <li>Give a <m>4 \times 4</m> matrix <m>Q</m> that may be used to perform the row operation <m> R_2 \leftrightarrow R_1 </m>.</li>
      <li>Use matrix multiplication to describe the matrix obtained by applying
              <m> R_2 \leftrightarrow R_1 </m> and then <m> R_4 \to R_4 + 3R_2 </m>
              to <m>A</m> (note the order).
          </li>
    </ol>
  </statement>
  <answer>
    <ol>
      <li>
        <m>B= \left[\begin{array}{cccc}
1 &amp; 0 &amp; 0 &amp; 0 \\
0 &amp; 1 &amp; 0 &amp; 0 \\
0 &amp; 0 &amp; 1 &amp; 0 \\
0 &amp; 3 &amp; 0 &amp; 1
\end{array}\right] </m>
      </li>
      <li>
        <m>Q= \left[\begin{array}{cccc}
0 &amp; 1 &amp; 0 &amp; 0 \\
1 &amp; 0 &amp; 0 &amp; 0 \\
0 &amp; 0 &amp; 1 &amp; 0 \\
0 &amp; 0 &amp; 0 &amp; 1
\end{array}\right] </m>
      </li>
      <li>
        <m>BQA</m>
      </li>
    </ol>
  </answer>
</exercise>