CoCalc -- 0009.ptx

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ubuntu2004
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<exercise checkit-seed="0009" checkit-slug="E2" checkit-title="Reduced row echelon form">
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  <statement>
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    <ol>
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      <li>Show that <me>\operatorname{RREF} \left[\begin{array}{ccc}
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4 &amp; 5 &amp; -3 \\
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4 &amp; 1 &amp; -7 \\
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5 &amp; 3 &amp; -7 \\
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-3 &amp; 5 &amp; 11 \\
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3 &amp; 5 &amp; -1
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\end{array}\right] = \left[\begin{array}{ccc}
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1 &amp; 0 &amp; -2 \\
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0 &amp; 1 &amp; 1 \\
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0 &amp; 0 &amp; 0 \\
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0 &amp; 0 &amp; 0 \\
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0 &amp; 0 &amp; 0
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\end{array}\right] .</me></li>
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      <li>Explain why the matrix <m>B= \left[\begin{array}{ccc}
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0 &amp; 1 &amp; -1 \\
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1 &amp; 0 &amp; 4 \\
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0 &amp; 0 &amp; 0 \\
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0 &amp; 0 &amp; 0 \\
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0 &amp; 0 &amp; 0
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\end{array}\right] </m> is or is not in reduced row echelon form.</li>
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    </ol>
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  </statement>
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  <answer>
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    <ol>
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      <li>
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        <m>\operatorname{RREF} \left[\begin{array}{ccc}
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4 &amp; 5 &amp; -3 \\
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4 &amp; 1 &amp; -7 \\
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5 &amp; 3 &amp; -7 \\
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-3 &amp; 5 &amp; 11 \\
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3 &amp; 5 &amp; -1
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\end{array}\right] = \left[\begin{array}{ccc}
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1 &amp; 0 &amp; -2 \\
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0 &amp; 1 &amp; 1 \\
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0 &amp; 0 &amp; 0 \\
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0 &amp; 0 &amp; 0 \\
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0 &amp; 0 &amp; 0
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\end{array}\right] .</m>
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      </li>
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      <li><m>B</m> is
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                        not in reduced row echelon form because
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                                the pivots are not descending to the right.
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                            </li>
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    </ol>
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  </answer>
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</exercise>
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