0008.ptx

<exercise checkit-seed="0008" checkit-slug="E1" checkit-title="Linear systems, vector equations, and augmented matrices">
  <statement>
    <p>Consider the vector equation.</p>
    <me> x_{1} \left[\begin{array}{c}
0 \\
-1 \\
-1 \\
-4
\end{array}\right] + x_{2} \left[\begin{array}{c}
-4 \\
2 \\
-3 \\
8
\end{array}\right] + x_{3} \left[\begin{array}{c}
4 \\
-2 \\
3 \\
-8
\end{array}\right] = \left[\begin{array}{c}
8 \\
-2 \\
8 \\
-8
\end{array}\right] </me>
    <ol>
      <li> Write a system of scalar equations corresponding to this vector equation. </li>
      <li> Write an augmented matrix corresponding to this vector equation. </li>
    </ol>
  </statement>
  <answer>
    <ol>
      <li>
        <me>\begin{matrix}
 &amp;  &amp; 4 \, x_{2} &amp;  +  &amp; 4 \, x_{3} &amp; = &amp; 8 \\
 -x_{1} &amp;  +  &amp; 2 \, x_{2} &amp;  -  &amp; 2 \, x_{3} &amp; = &amp; -2 \\
 -x_{1} &amp;  -  &amp; 3 \, x_{2} &amp;  +  &amp; 3 \, x_{3} &amp; = &amp; 8 \\
 -4 \, x_{1} &amp;  +  &amp; 8 \, x_{2} &amp;  -  &amp; 8 \, x_{3} &amp; = &amp; -8 \\
 \end{matrix}</me>
      </li>
      <li>
        <me> \left[\begin{array}{ccc|c}
0 &amp; -4 &amp; 4 &amp; 8 \\
-1 &amp; 2 &amp; -2 &amp; -2 \\
-1 &amp; -3 &amp; 3 &amp; 8 \\
-4 &amp; 8 &amp; -8 &amp; -8
\end{array}\right] </me>
      </li>
    </ol>
  </answer>
</exercise>