0005.qti

<item ident="M2-0005" title="M2 | Row operations as matrix multiplication | ver. 0005">
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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?P" alt="P" title="P" data-latex="P"/> 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_1 \to 3R_1" alt="R_1 \to 3R_1" title="R_1 \to 3R_1" data-latex="R_1 \to 3R_1"/>.</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?N" alt="N" title="N" data-latex="N"/> 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_1 \to R_1 + 4R_3" alt="R_1 \to R_1 + 4R_3" title="R_1 \to R_1 + 4R_3" data-latex="R_1 \to R_1 + 4R_3"/>.</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_1 \to R_1 + 4R_3" alt="R_1 \to R_1 + 4R_3" title="R_1 \to R_1 + 4R_3" data-latex="R_1 \to R_1 + 4R_3"/> and then <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?R_1 \to 3R_1" alt="R_1 \to 3R_1" title="R_1 \to 3R_1" data-latex="R_1 \to 3R_1"/> 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?P" alt="P" title="P" data-latex="P"&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_1%20%5Cto%203R_1" alt="R_1 \to 3R_1" title="R_1 \to 3R_1" data-latex="R_1 \to 3R_1"&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?N" alt="N" title="N" data-latex="N"&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_1%20%5Cto%20R_1%20+%204R_3" alt="R_1 \to R_1 + 4R_3" title="R_1 \to R_1 + 4R_3" data-latex="R_1 \to R_1 + 4R_3"&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_1%20%5Cto%20R_1%20+%204R_3" alt="R_1 \to R_1 + 4R_3" title="R_1 \to R_1 + 4R_3" data-latex="R_1 \to R_1 + 4R_3"&gt; and then &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?R_1%20%5Cto%203R_1" alt="R_1 \to 3R_1" title="R_1 \to 3R_1" data-latex="R_1 \to 3R_1"&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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        <response_label ident="answer1" rshuffle="No"/>
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  <itemfeedback ident="general_fb">
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            <h4>Partial Answer:</h4>
            <ol type="a">
              <li>
                <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?P= \left[\begin{array}{cccc} 3 &amp; 0 &amp; 0 &amp; 0 \\ 0 &amp; 1 &amp; 0 &amp; 0 \\ 0 &amp; 0 &amp; 1 &amp; 0 \\ 0 &amp; 0 &amp; 0 &amp; 1 \end{array}\right]" alt="P= \left[\begin{array}{cccc} 3 &amp; 0 &amp; 0 &amp; 0 \\ 0 &amp; 1 &amp; 0 &amp; 0 \\ 0 &amp; 0 &amp; 1 &amp; 0 \\ 0 &amp; 0 &amp; 0 &amp; 1 \end{array}\right]" title="P= \left[\begin{array}{cccc} 3 &amp; 0 &amp; 0 &amp; 0 \\ 0 &amp; 1 &amp; 0 &amp; 0 \\ 0 &amp; 0 &amp; 1 &amp; 0 \\ 0 &amp; 0 &amp; 0 &amp; 1 \end{array}\right]" data-latex="P= \left[\begin{array}{cccc} 3 &amp; 0 &amp; 0 &amp; 0 \\ 0 &amp; 1 &amp; 0 &amp; 0 \\ 0 &amp; 0 &amp; 1 &amp; 0 \\ 0 &amp; 0 &amp; 0 &amp; 1 \end{array}\right]"/>
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              <li>
                <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?N= \left[\begin{array}{cccc} 1 &amp; 0 &amp; 4 &amp; 0 \\ 0 &amp; 1 &amp; 0 &amp; 0 \\ 0 &amp; 0 &amp; 1 &amp; 0 \\ 0 &amp; 0 &amp; 0 &amp; 1 \end{array}\right]" alt="N= \left[\begin{array}{cccc} 1 &amp; 0 &amp; 4 &amp; 0 \\ 0 &amp; 1 &amp; 0 &amp; 0 \\ 0 &amp; 0 &amp; 1 &amp; 0 \\ 0 &amp; 0 &amp; 0 &amp; 1 \end{array}\right]" title="N= \left[\begin{array}{cccc} 1 &amp; 0 &amp; 4 &amp; 0 \\ 0 &amp; 1 &amp; 0 &amp; 0 \\ 0 &amp; 0 &amp; 1 &amp; 0 \\ 0 &amp; 0 &amp; 0 &amp; 1 \end{array}\right]" data-latex="N= \left[\begin{array}{cccc} 1 &amp; 0 &amp; 4 &amp; 0 \\ 0 &amp; 1 &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?PNA" alt="PNA" title="PNA" data-latex="PNA"/>
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        <mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;ol type="a"&gt;
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      &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?P=%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D%203%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;%200%20&amp;amp;%200%20&amp;amp;%201%20%5Cend%7Barray%7D%5Cright%5D" alt="P= \left[\begin{array}{cccc} 3 &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; 0 &amp;amp; 0 &amp;amp; 1 \end{array}\right]" title="P= \left[\begin{array}{cccc} 3 &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; 0 &amp;amp; 0 &amp;amp; 1 \end{array}\right]" data-latex="P= \left[\begin{array}{cccc} 3 &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; 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?N=%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D%201%20&amp;amp;%200%20&amp;amp;%204%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;%200%20&amp;amp;%200%20&amp;amp;%201%20%5Cend%7Barray%7D%5Cright%5D" alt="N= \left[\begin{array}{cccc} 1 &amp;amp; 0 &amp;amp; 4 &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; 0 &amp;amp; 0 &amp;amp; 1 \end{array}\right]" title="N= \left[\begin{array}{cccc} 1 &amp;amp; 0 &amp;amp; 4 &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; 0 &amp;amp; 0 &amp;amp; 1 \end{array}\right]" data-latex="N= \left[\begin{array}{cccc} 1 &amp;amp; 0 &amp;amp; 4 &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; 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?PNA" alt="PNA" title="PNA" data-latex="PNA"&gt;
    &lt;/li&gt;
  &lt;/ol&gt;
&lt;/div&gt;

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