0002.ptx

<exercise checkit-seed="0002" checkit-slug="E1" checkit-title="Linear systems, vector equations, and augmented matrices">
  <statement>
    <p> Consider the augmented matrix </p>
    <me> \left[\begin{array}{ccc|c}
4 &amp; 1 &amp; 7 &amp; 6 \\
-5 &amp; -4 &amp; -6 &amp; -2 \\
-1 &amp; 1 &amp; -3 &amp; -4 \\
-3 &amp; 0 &amp; -6 &amp; -6
\end{array}\right] </me>
    <ol>
      <li> Write a system of scalar equations corresponding to this augmented matrix. </li>
      <li> Write a vector equation corresponding to this augmented matrix. </li>
    </ol>
  </statement>
  <answer>
    <ol>
      <li>
        <me>\begin{matrix}
 4 \, x_{1} &amp;  +  &amp; x_{2} &amp;  +  &amp; 7 \, x_{3} &amp; = &amp; 6 \\
 -5 \, x_{1} &amp;  -  &amp; 4 \, x_{2} &amp;  -  &amp; 6 \, x_{3} &amp; = &amp; -2 \\
 -x_{1} &amp;  +  &amp; x_{2} &amp;  -  &amp; 3 \, x_{3} &amp; = &amp; -4 \\
 -3 \, x_{1} &amp;  &amp;  &amp;  -  &amp; 6 \, x_{3} &amp; = &amp; -6 \\
 \end{matrix}</me>
      </li>
      <li>
        <me> x_{1} \left[\begin{array}{c}
4 \\
-5 \\
-1 \\
-3
\end{array}\right] + x_{2} \left[\begin{array}{c}
1 \\
-4 \\
1 \\
0
\end{array}\right] + x_{3} \left[\begin{array}{c}
7 \\
-6 \\
-3 \\
-6
\end{array}\right] = \left[\begin{array}{c}
6 \\
-2 \\
-4 \\
-6
\end{array}\right] </me>
      </li>
    </ol>
  </answer>
</exercise>