<div class="checkit exercise" data-checkit-slug="A2" data-checkit-title="Standard matrices" data-checkit-seed="0004">
  <div class="exercise-statement">
    <ol type="a">
      <li>Find the standard matrix for the linear transformation <span class="math math-inline">\(S:\mathbb{R}^ 4  \to \mathbb{R}^ 2 \)</span> given by <p class="math math-display">\[S\left(  \left[\begin{array}{c}
x \\
y \\
z \\
{w}
\end{array}\right]  \right) =  \left[\begin{array}{c}
2 \, x - 3 \, y + z + 6 \, {w} \\
x - y + 2 \, {w}
\end{array}\right] .\]</p></li>
      <li>Let <span class="math math-inline">\(T:\mathbb{R}^ 4  \to \mathbb{R}^ 3 \)</span> be the linear transformation given by the standard matrix <p class="math math-display">\[ \left[\begin{array}{cccc}
3 &amp; 0 &amp; 4 &amp; 5 \\
0 &amp; 1 &amp; 1 &amp; 3 \\
-1 &amp; -1 &amp; -2 &amp; -4
\end{array}\right] .\]</p> Compute <span class="math math-inline">\(T\left( \left[\begin{array}{c}
5 \\
8 \\
7 \\
-2
\end{array}\right]  \right)\)</span>. </li>
    </ol>
  </div>
  <div class="exercise-answer">
    <p>
      <b>Answer:</b>
    </p>
    <ol type="a">
      <li>
        <p class="math math-display">\[ \left[\begin{array}{cccc}
2 &amp; -3 &amp; 1 &amp; 6 \\
1 &amp; -1 &amp; 0 &amp; 2
\end{array}\right] \]</p>
      </li>
      <li>
        <p class="math math-display">\[T\left( \left[\begin{array}{c}
5 \\
8 \\
7 \\
-2
\end{array}\right]  \right)= \left[\begin{array}{c}
33 \\
9 \\
-19
\end{array}\right] \]</p>
      </li>
    </ol>
  </div>
</div>



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