0004.ptx

<exercise checkit-seed="0004" checkit-slug="G1" checkit-title="Row operations and determinants">
  <statement>
    <p>Let <m>A</m> be a <m>4 \times 4</m> matrix with determinant <m> 6 </m>.</p>
    <ol>
      <li>Let <m>N</m> be the matrix obtained from <m>A</m> by applying the row operation <m> R_3 \to -3R_3 </m>.
              What is <m>\operatorname{det}\ N</m>?</li>
      <li>Let <m>Q</m> be the matrix obtained from <m>A</m> by applying the row operation <m> R_1 \leftrightarrow R_2 </m>.
              What is <m>\operatorname{det}\ Q</m>?</li>
      <li>Let <m>C</m> be the matrix obtained from <m>A</m> by applying the row operation <m> R_1 \to R_1 + 5R_2 </m>.
              What is <m>\operatorname{det}\ C</m>?</li>
    </ol>
  </statement>
  <answer>
    <ol>
      <li>
        <m>\operatorname{det}\ N= -18 </m>
      </li>
      <li>
        <m>\operatorname{det}\ Q= -6 </m>
      </li>
      <li>
        <m>\operatorname{det}\ C= 6 </m>
      </li>
    </ol>
  </answer>
</exercise>