A2-0.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>