0010.ptx

<exercise checkit-seed="0010" 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}
1 \\
0 \\
1 \\
0
\end{array}\right] + x_{2} \left[\begin{array}{c}
6 \\
1 \\
-1 \\
2
\end{array}\right] + x_{3} \left[\begin{array}{c}
5 \\
2 \\
-4 \\
2
\end{array}\right] = \left[\begin{array}{c}
-7 \\
-1 \\
0 \\
-2
\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}
 x &amp;  +  &amp; 6 \, y &amp;  +  &amp; 5 \, z &amp; = &amp; -7 \\
 &amp;  &amp; y &amp;  +  &amp; 2 \, z &amp; = &amp; -1 \\
 x &amp;  -  &amp; y &amp;  -  &amp; 4 \, z &amp; = &amp; 0 \\
 &amp;  &amp; 2 \, y &amp;  +  &amp; 2 \, z &amp; = &amp; -2 \\
 \end{matrix}</me>
      </li>
      <li>
        <me> \left[\begin{array}{ccc|c}
1 &amp; 6 &amp; 5 &amp; -7 \\
0 &amp; 1 &amp; 2 &amp; -1 \\
1 &amp; -1 &amp; -4 &amp; 0 \\
0 &amp; 2 &amp; 2 &amp; -2
\end{array}\right] </me>
      </li>
    </ol>
  </answer>
</exercise>