0000.ptx

<exercise checkit-seed="0000" checkit-slug="A2" checkit-title="Standard matrices">
  <statement>
    <ol>
      <li>Find the standard matrix for the linear transformation <m>S:\mathbb{R}^ 2  \to \mathbb{R}^ 4 </m> given by
              <me>S\left(  \left[\begin{array}{c}
x \\
y
\end{array}\right]  \right) =  \left[\begin{array}{c}
x - 5 \, y \\
-x + 6 \, y \\
0 \\
x - 2 \, y
\end{array}\right] .</me></li>
      <li>Let <m>T:\mathbb{R}^ 2  \to \mathbb{R}^ 4 </m> be the linear transformation given by the standard matrix
              <me> \left[\begin{array}{cc}
-1 &amp; 0 \\
-1 &amp; -4 \\
2 &amp; 5 \\
-1 &amp; 0
\end{array}\right] .</me>
              Compute <m>T\left( \left[\begin{array}{c}
-2 \\
8
\end{array}\right]  \right)</m>.
          </li>
    </ol>
  </statement>
  <answer>
    <ol>
      <li>
        <me> \left[\begin{array}{cc}
1 &amp; -5 \\
-1 &amp; 6 \\
0 &amp; 0 \\
1 &amp; -2
\end{array}\right] </me>
      </li>
      <li>
        <me>T\left( \left[\begin{array}{c}
-2 \\
8
\end{array}\right]  \right)= \left[\begin{array}{c}
2 \\
-30 \\
36 \\
2
\end{array}\right] </me>
      </li>
    </ol>
  </answer>
</exercise>