0002.ptx

<exercise checkit-seed="0002" checkit-slug="E2" checkit-title="Reduced row echelon form">
  <statement>
    <ol>
      <li>Show that <me>\operatorname{RREF} \left[\begin{array}{ccc}
3 &amp; -10 &amp; 0 \\
-2 &amp; 7 &amp; 0 \\
1 &amp; 2 &amp; 0 \\
2 &amp; -7 &amp; 0 \\
3 &amp; -9 &amp; 0
\end{array}\right] = \left[\begin{array}{ccc}
1 &amp; 0 &amp; 0 \\
0 &amp; 1 &amp; 0 \\
0 &amp; 0 &amp; 0 \\
0 &amp; 0 &amp; 0 \\
0 &amp; 0 &amp; 0
\end{array}\right] .</me></li>
      <li>Explain why the matrix <m>B= \left[\begin{array}{ccc}
1 &amp; 0 &amp; -2 \\
-2 &amp; 1 &amp; 4 \\
0 &amp; 0 &amp; 0 \\
0 &amp; 0 &amp; 0 \\
0 &amp; 0 &amp; 0
\end{array}\right] </m> is or is not in reduced row echelon form.</li>
    </ol>
  </statement>
  <answer>
    <ol>
      <li>
        <m>\operatorname{RREF} \left[\begin{array}{ccc}
3 &amp; -10 &amp; 0 \\
-2 &amp; 7 &amp; 0 \\
1 &amp; 2 &amp; 0 \\
2 &amp; -7 &amp; 0 \\
3 &amp; -9 &amp; 0
\end{array}\right] = \left[\begin{array}{ccc}
1 &amp; 0 &amp; 0 \\
0 &amp; 1 &amp; 0 \\
0 &amp; 0 &amp; 0 \\
0 &amp; 0 &amp; 0 \\
0 &amp; 0 &amp; 0
\end{array}\right] .</m>
      </li>
      <li><m>B</m> is
                
                        not in reduced row echelon form because
                        
                                not every entry above and below each pivot is zero.
                            </li>
    </ol>
  </answer>
</exercise>