E1-0.ptx

<exercise checkit-seed="0000" 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 \\
-3 \\
3
\end{array}\right] + x_{2} \left[\begin{array}{c}
4 \\
-3 \\
3
\end{array}\right] + x_{3} \left[\begin{array}{c}
3 \\
1 \\
3
\end{array}\right] + x_{4} \left[\begin{array}{c}
18 \\
-7 \\
15
\end{array}\right] = \left[\begin{array}{c}
-11 \\
5 \\
-9
\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; 3 \, x_{3} &amp;  +  &amp; 18 \, x_{4} &amp; = &amp; -11 \\
 -3 \, x_{1} &amp;  -  &amp; 3 \, x_{2} &amp;  +  &amp; x_{3} &amp;  -  &amp; 7 \, x_{4} &amp; = &amp; 5 \\
 3 \, x_{1} &amp;  +  &amp; 3 \, x_{2} &amp;  +  &amp; 3 \, x_{3} &amp;  +  &amp; 15 \, x_{4} &amp; = &amp; -9 \\
 \end{matrix}</me></li>
                <li><me>\left[\begin{array}{cccc|c}
4 &amp; 4 &amp; 3 &amp; 18 &amp; -11 \\
-3 &amp; -3 &amp; 1 &amp; -7 &amp; 5 \\
3 &amp; 3 &amp; 3 &amp; 15 &amp; -9
\end{array}\right]</me></li>
      </ol>
    </answer>
</exercise>