0005.ptx

<exercise checkit-seed="0005" checkit-slug="M3" checkit-title="Invertible matrices">
  <statement>
    <p>Explain why the matrix <m>Q= \left[\begin{array}{cccc}
-1 &amp; 1 &amp; -1 &amp; 2 \\
-2 &amp; 3 &amp; -5 &amp; 5 \\
1 &amp; -1 &amp; 1 &amp; -2 \\
3 &amp; -1 &amp; -3 &amp; -4
\end{array}\right] </m> is or is not invertible.</p>
  </statement>
  <answer><p><me>\operatorname{RREF} \left[\begin{array}{cccc}
-1 &amp; 1 &amp; -1 &amp; 2 \\
-2 &amp; 3 &amp; -5 &amp; 5 \\
1 &amp; -1 &amp; 1 &amp; -2 \\
3 &amp; -1 &amp; -3 &amp; -4
\end{array}\right] = \left[\begin{array}{cccc}
1 &amp; 0 &amp; -2 &amp; -1 \\
0 &amp; 1 &amp; -3 &amp; 1 \\
0 &amp; 0 &amp; 0 &amp; 0 \\
0 &amp; 0 &amp; 0 &amp; 0
\end{array}\right] </me></p><m>Q</m> is not invertible.</answer>
</exercise>