E1-9.ptx

<exercise checkit-seed="0009" checkit-slug="E1" checkit-title="Linear systems, vector equations, and augmented matrices">
  <statement>
        <p> Consider the system of equations</p>
              <me>\begin{matrix}
 -x_{1} &amp;  &amp;  &amp;  +  &amp; 3 \, x_{3} &amp; = &amp; -11 \\
 3 \, x_{1} &amp;  +  &amp; x_{2} &amp;  -  &amp; x_{3} &amp; = &amp; 6 \\
 -2 \, x_{1} &amp;  &amp;  &amp;  +  &amp; 5 \, x_{3} &amp; = &amp; -19 \\
 &amp;  &amp;  &amp;  &amp; 2 \, x_{3} &amp; = &amp; -6 \\
 \end{matrix}</me>
        <ol>
            <li> Write an augmented matrix corresponding to this system. </li>
            <li> Write a vector equation corresponding to this system. </li>
        </ol>
  </statement>

  <answer>
     <ol>
                <li><me>\left[\begin{array}{ccc|c}
-1 &amp; 0 &amp; 3 &amp; -11 \\
3 &amp; 1 &amp; -1 &amp; 6 \\
-2 &amp; 0 &amp; 5 &amp; -19 \\
0 &amp; 0 &amp; 2 &amp; -6
\end{array}\right]</me></li>
                <li><me>x_{1} \left[\begin{array}{c}
-1 \\
3 \\
-2 \\
0
\end{array}\right] + x_{2} \left[\begin{array}{c}
0 \\
1 \\
0 \\
0
\end{array}\right] + x_{3} \left[\begin{array}{c}
3 \\
-1 \\
5 \\
2
\end{array}\right] = \left[\begin{array}{c}
-11 \\
6 \\
-19 \\
-6
\end{array}\right]</me></li>
      </ol>
    </answer>
</exercise>