0007.ptx

<exercise checkit-seed="0007" 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>P</m> be the matrix obtained from <m>A</m> by applying the row operation <m> R_4 \to R_4 + 5R_1 </m>.
              What is <m>\operatorname{det}\ P</m>?</li>
      <li>Let <m>B</m> be the matrix obtained from <m>A</m> by applying the row operation <m> R_2 \leftrightarrow R_1 </m>.
              What is <m>\operatorname{det}\ B</m>?</li>
      <li>Let <m>M</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}\ M</m>?</li>
    </ol>
  </statement>
  <answer>
    <ol>
      <li>
        <m>\operatorname{det}\ P= 6 </m>
      </li>
      <li>
        <m>\operatorname{det}\ B= -6 </m>
      </li>
      <li>
        <m>\operatorname{det}\ M= 18 </m>
      </li>
    </ol>
  </answer>
</exercise>