E1-2.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}
-5 &amp; -3 &amp; 18 &amp; -14 \\
-3 &amp; -2 &amp; 11 &amp; -9 \\
-1 &amp; 3 &amp; 0 &amp; 8 \\
0 &amp; -1 &amp; 1 &amp; -3
\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}
 -5 \, x_{1} &amp;  -  &amp; 3 \, x_{2} &amp;  +  &amp; 18 \, x_{3} &amp; = &amp; -14 \\
 -3 \, x_{1} &amp;  -  &amp; 2 \, x_{2} &amp;  +  &amp; 11 \, x_{3} &amp; = &amp; -9 \\
 -x_{1} &amp;  +  &amp; 3 \, x_{2} &amp;  &amp;  &amp; = &amp; 8 \\
 &amp;  -  &amp; x_{2} &amp;  +  &amp; x_{3} &amp; = &amp; -3 \\
 \end{matrix}</me></li>
                <li><me>x_{1} \left[\begin{array}{c}
-5 \\
-3 \\
-1 \\
0
\end{array}\right] + x_{2} \left[\begin{array}{c}
-3 \\
-2 \\
3 \\
-1
\end{array}\right] + x_{3} \left[\begin{array}{c}
18 \\
11 \\
0 \\
1
\end{array}\right] = \left[\begin{array}{c}
-14 \\
-9 \\
8 \\
-3
\end{array}\right]</me></li>
      </ol>
    </answer>
</exercise>