E1-3.ptx

<exercise checkit-seed="0003" checkit-slug="E1" checkit-title="Linear systems, vector equations, and augmented matrices">
  <statement>
        <p> Consider the system of equations</p>
              <me>\begin{matrix}
 x &amp;  -  &amp; y &amp;  +  &amp; 4 \, z &amp; = &amp; 4 \\
 2 \, x &amp;  -  &amp; y &amp;  +  &amp; 4 \, z &amp; = &amp; 7 \\
 &amp;  -  &amp; y &amp;  +  &amp; 5 \, z &amp; = &amp; 1 \\
 &amp;  &amp;  &amp;  -  &amp; 2 \, z &amp; = &amp; 0 \\
 \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; -1 &amp; 4 &amp; 4 \\
2 &amp; -1 &amp; 4 &amp; 7 \\
0 &amp; -1 &amp; 5 &amp; 1 \\
0 &amp; 0 &amp; -2 &amp; 0
\end{array}\right]</me></li>
                <li><me>x_{1} \left[\begin{array}{c}
1 \\
2 \\
0 \\
0
\end{array}\right] + x_{2} \left[\begin{array}{c}
-1 \\
-1 \\
-1 \\
0
\end{array}\right] + x_{3} \left[\begin{array}{c}
4 \\
4 \\
5 \\
-2
\end{array}\right] = \left[\begin{array}{c}
4 \\
7 \\
1 \\
0
\end{array}\right]</me></li>
      </ol>
    </answer>
</exercise>