0011.qti

<item ident="M2-0011" title="M2 | Row operations as matrix multiplication | ver. 0011">
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  <presentation>
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        <div class="exercise-statement">
          <p>
            <strong>M2.</strong>
          </p>
          <p>Let <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?A" alt="A" title="A" data-latex="A"/> be a <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?4 \times 4" alt="4 \times 4" title="4 \times 4" data-latex="4 \times 4"/> matrix.</p>
          <ol type="a">
            <li>Give a <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?4 \times 4" alt="4 \times 4" title="4 \times 4" data-latex="4 \times 4"/> matrix <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?B" alt="B" title="B" data-latex="B"/> that may be used to perform the row operation <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?R_4 \to R_4 + 3R_2" alt="R_4 \to R_4 + 3R_2" title="R_4 \to R_4 + 3R_2" data-latex="R_4 \to R_4 + 3R_2"/>.</li>
            <li>Give a <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?4 \times 4" alt="4 \times 4" title="4 \times 4" data-latex="4 \times 4"/> matrix <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?Q" alt="Q" title="Q" data-latex="Q"/> that may be used to perform the row operation <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?R_2 \leftrightarrow R_1" alt="R_2 \leftrightarrow R_1" title="R_2 \leftrightarrow R_1" data-latex="R_2 \leftrightarrow R_1"/>.</li>
            <li>Use matrix multiplication to describe the matrix obtained by applying <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?R_2 \leftrightarrow R_1" alt="R_2 \leftrightarrow R_1" title="R_2 \leftrightarrow R_1" data-latex="R_2 \leftrightarrow R_1"/> and then <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?R_4 \to R_4 + 3R_2" alt="R_4 \to R_4 + 3R_2" title="R_4 \to R_4 + 3R_2" data-latex="R_4 \to R_4 + 3R_2"/> to <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?A" alt="A" title="A" data-latex="A"/> (note the order). </li>
          </ol>
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      <mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;M2.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Let &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?A" alt="A" title="A" data-latex="A"&gt; be a &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?4%20%5Ctimes%204" alt="4 \times 4" title="4 \times 4" data-latex="4 \times 4"&gt; matrix.&lt;/p&gt;
  &lt;ol type="a"&gt;
    &lt;li&gt;Give a &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?4%20%5Ctimes%204" alt="4 \times 4" title="4 \times 4" data-latex="4 \times 4"&gt; matrix &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?B" alt="B" title="B" data-latex="B"&gt; that may be used to perform the row operation &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?R_4%20%5Cto%20R_4%20+%203R_2" alt="R_4 \to R_4 + 3R_2" title="R_4 \to R_4 + 3R_2" data-latex="R_4 \to R_4 + 3R_2"&gt;.&lt;/li&gt;
    &lt;li&gt;Give a &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?4%20%5Ctimes%204" alt="4 \times 4" title="4 \times 4" data-latex="4 \times 4"&gt; matrix &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?Q" alt="Q" title="Q" data-latex="Q"&gt; that may be used to perform the row operation &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?R_2%20%5Cleftrightarrow%20R_1" alt="R_2 \leftrightarrow R_1" title="R_2 \leftrightarrow R_1" data-latex="R_2 \leftrightarrow R_1"&gt;.&lt;/li&gt;
    &lt;li&gt;Use matrix multiplication to describe the matrix obtained by applying &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?R_2%20%5Cleftrightarrow%20R_1" alt="R_2 \leftrightarrow R_1" title="R_2 \leftrightarrow R_1" data-latex="R_2 \leftrightarrow R_1"&gt; and then &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?R_4%20%5Cto%20R_4%20+%203R_2" alt="R_4 \to R_4 + 3R_2" title="R_4 \to R_4 + 3R_2" data-latex="R_4 \to R_4 + 3R_2"&gt; to &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?A" alt="A" title="A" data-latex="A"&gt; (note the order). &lt;/li&gt;
  &lt;/ol&gt;
&lt;/div&gt;

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    <response_str ident="response1" rcardinality="Single">
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  <itemfeedback ident="general_fb">
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            <h4>Partial Answer:</h4>
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              <li>
                <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?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]" alt="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]" title="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]" data-latex="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]"/>
              </li>
              <li>
                <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?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]" alt="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]" title="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]" data-latex="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]"/>
              </li>
              <li>
                <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?BQA" alt="BQA" title="BQA" data-latex="BQA"/>
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        <mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
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    &lt;li&gt;
      &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?B=%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D%201%20&amp;amp;%200%20&amp;amp;%200%20&amp;amp;%200%20%5C%5C%200%20&amp;amp;%201%20&amp;amp;%200%20&amp;amp;%200%20%5C%5C%200%20&amp;amp;%200%20&amp;amp;%201%20&amp;amp;%200%20%5C%5C%200%20&amp;amp;%203%20&amp;amp;%200%20&amp;amp;%201%20%5Cend%7Barray%7D%5Cright%5D" alt="B= \left[\begin{array}{cccc} 1 &amp;amp; 0 &amp;amp; 0 &amp;amp; 0 \\ 0 &amp;amp; 1 &amp;amp; 0 &amp;amp; 0 \\ 0 &amp;amp; 0 &amp;amp; 1 &amp;amp; 0 \\ 0 &amp;amp; 3 &amp;amp; 0 &amp;amp; 1 \end{array}\right]" title="B= \left[\begin{array}{cccc} 1 &amp;amp; 0 &amp;amp; 0 &amp;amp; 0 \\ 0 &amp;amp; 1 &amp;amp; 0 &amp;amp; 0 \\ 0 &amp;amp; 0 &amp;amp; 1 &amp;amp; 0 \\ 0 &amp;amp; 3 &amp;amp; 0 &amp;amp; 1 \end{array}\right]" data-latex="B= \left[\begin{array}{cccc} 1 &amp;amp; 0 &amp;amp; 0 &amp;amp; 0 \\ 0 &amp;amp; 1 &amp;amp; 0 &amp;amp; 0 \\ 0 &amp;amp; 0 &amp;amp; 1 &amp;amp; 0 \\ 0 &amp;amp; 3 &amp;amp; 0 &amp;amp; 1 \end{array}\right]"&gt;
    &lt;/li&gt;
    &lt;li&gt;
      &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?Q=%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D%200%20&amp;amp;%201%20&amp;amp;%200%20&amp;amp;%200%20%5C%5C%201%20&amp;amp;%200%20&amp;amp;%200%20&amp;amp;%200%20%5C%5C%200%20&amp;amp;%200%20&amp;amp;%201%20&amp;amp;%200%20%5C%5C%200%20&amp;amp;%200%20&amp;amp;%200%20&amp;amp;%201%20%5Cend%7Barray%7D%5Cright%5D" alt="Q= \left[\begin{array}{cccc} 0 &amp;amp; 1 &amp;amp; 0 &amp;amp; 0 \\ 1 &amp;amp; 0 &amp;amp; 0 &amp;amp; 0 \\ 0 &amp;amp; 0 &amp;amp; 1 &amp;amp; 0 \\ 0 &amp;amp; 0 &amp;amp; 0 &amp;amp; 1 \end{array}\right]" title="Q= \left[\begin{array}{cccc} 0 &amp;amp; 1 &amp;amp; 0 &amp;amp; 0 \\ 1 &amp;amp; 0 &amp;amp; 0 &amp;amp; 0 \\ 0 &amp;amp; 0 &amp;amp; 1 &amp;amp; 0 \\ 0 &amp;amp; 0 &amp;amp; 0 &amp;amp; 1 \end{array}\right]" data-latex="Q= \left[\begin{array}{cccc} 0 &amp;amp; 1 &amp;amp; 0 &amp;amp; 0 \\ 1 &amp;amp; 0 &amp;amp; 0 &amp;amp; 0 \\ 0 &amp;amp; 0 &amp;amp; 1 &amp;amp; 0 \\ 0 &amp;amp; 0 &amp;amp; 0 &amp;amp; 1 \end{array}\right]"&gt;
    &lt;/li&gt;
    &lt;li&gt;
      &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?BQA" alt="BQA" title="BQA" data-latex="BQA"&gt;
    &lt;/li&gt;
  &lt;/ol&gt;
&lt;/div&gt;

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