<div class="checkit exercise" data-checkit-slug="E1" data-checkit-title="Linear systems, vector equations, and augmented matrices" data-checkit-seed="0009">
  <div class="exercise-statement">
    <p> Consider the system of equations</p>
    <p class="math math-display">\[\begin{matrix}
 x_{1} &amp;  &amp;  &amp;  +  &amp; 3 \, x_{3} &amp; = &amp; -4 \\
 &amp;  &amp; x_{2} &amp;  +  &amp; 3 \, x_{3} &amp; = &amp; -5 \\
 x_{1} &amp;  &amp;  &amp;  +  &amp; 4 \, x_{3} &amp; = &amp; -6 \\
 3 \, x_{1} &amp;  -  &amp; 2 \, x_{2} &amp;  +  &amp; 6 \, x_{3} &amp; = &amp; -8 \\
 \end{matrix}\]</p>
    <ol type="a">
      <li> Write an augmented matrix corresponding to this system. </li>
      <li> Write a vector equation corresponding to this system. </li>
    </ol>
  </div>
  <div class="exercise-answer">
    <p>
      <b>Answer:</b>
    </p>
    <ol type="a">
      <li>
        <p class="math math-display">\[ \left[\begin{array}{ccc|c}
1 &amp; 0 &amp; 3 &amp; -4 \\
0 &amp; 1 &amp; 3 &amp; -5 \\
1 &amp; 0 &amp; 4 &amp; -6 \\
3 &amp; -2 &amp; 6 &amp; -8
\end{array}\right] \]</p>
      </li>
      <li>
        <p class="math math-display">\[ x_{1} \left[\begin{array}{c}
1 \\
0 \\
1 \\
3
\end{array}\right] + x_{2} \left[\begin{array}{c}
0 \\
1 \\
0 \\
-2
\end{array}\right] + x_{3} \left[\begin{array}{c}
3 \\
3 \\
4 \\
6
\end{array}\right] = \left[\begin{array}{c}
-4 \\
-5 \\
-6 \\
-8
\end{array}\right] \]</p>
      </li>
    </ol>
  </div>
</div>



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