<div class="checkit exercise" data-checkit-slug="A2" data-checkit-title="Standard matrices" data-checkit-seed="0010">
  <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">\[S\left(  \left[\begin{array}{c}
x_{1} \\
x_{2} \\
x_{3} \\
x_{4}
\end{array}\right]  \right) =  \left[\begin{array}{c}
x_{1} + 2 \, x_{2} - 4 \, x_{3} - x_{4} \\
-2 \, x_{1} - 3 \, x_{2} + 6 \, x_{3}
\end{array}\right] .\]</p></li>
      <li>Let <span class="math math-inline">\(T:\mathbb{R}^ 4  \to \mathbb{R}^ 1 \)</span> be the linear transformation given by the standard matrix <p class="math math-display">\[ \left[\begin{array}{cccc}
1 &amp; 2 &amp; -3 &amp; -3
\end{array}\right] .\]</p> Compute <span class="math math-inline">\(T\left( \left[\begin{array}{c}
-7 \\
-7 \\
-2 \\
2
\end{array}\right]  \right)\)</span>. </li>
    </ol>
  </div>
  <div class="exercise-answer">
    <p>
      <b>Answer:</b>
    </p>
    <ol type="a">
      <li>
        <p class="math math-display">\[ \left[\begin{array}{cccc}
1 &amp; 2 &amp; -4 &amp; -1 \\
-2 &amp; -3 &amp; 6 &amp; 0
\end{array}\right] \]</p>
      </li>
      <li>
        <p class="math math-display">\[T\left( \left[\begin{array}{c}
-7 \\
-7 \\
-2 \\
2
\end{array}\right]  \right)= \left[\begin{array}{c}
-21
\end{array}\right] \]</p>
      </li>
    </ol>
  </div>
</div>



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