E1-8.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}
-4 \\
5 \\
-4 \\
2
\end{array}\right] + x_{2} \left[\begin{array}{c}
-4 \\
5 \\
-4 \\
2
\end{array}\right] + x_{3} \left[\begin{array}{c}
-1 \\
1 \\
2 \\
4
\end{array}\right] = \left[\begin{array}{c}
-5 \\
7 \\
-14 \\
-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}
 -4 \, x_{1} &amp;  -  &amp; 4 \, x_{2} &amp;  -  &amp; x_{3} &amp; = &amp; -5 \\
 5 \, x_{1} &amp;  +  &amp; 5 \, x_{2} &amp;  +  &amp; x_{3} &amp; = &amp; 7 \\
 -4 \, x_{1} &amp;  -  &amp; 4 \, x_{2} &amp;  +  &amp; 2 \, x_{3} &amp; = &amp; -14 \\
 2 \, x_{1} &amp;  +  &amp; 2 \, x_{2} &amp;  +  &amp; 4 \, x_{3} &amp; = &amp; -8 \\
 \end{matrix}</me></li>
                <li><me>\left[\begin{array}{ccc|c}
-4 &amp; -4 &amp; -1 &amp; -5 \\
5 &amp; 5 &amp; 1 &amp; 7 \\
-4 &amp; -4 &amp; 2 &amp; -14 \\
2 &amp; 2 &amp; 4 &amp; -8
\end{array}\right]</me></li>
      </ol>
    </answer>
</exercise>