0010.ptx

<exercise checkit-seed="0010" checkit-slug="E3" checkit-title="Solving linear systems">
  <statement>
    <p>Show how to find the solution set for the following 
    
        vector equation <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></p>
  </statement>
  <answer>
    <me>\mathrm{RREF} \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]  =  \left[\begin{array}{ccc|c}
1 &amp; 0 &amp; 0 &amp; -1 \\
0 &amp; 1 &amp; 0 &amp; -1 \\
0 &amp; 0 &amp; 1 &amp; 0 \\
0 &amp; 0 &amp; 0 &amp; 0
\end{array}\right] </me>
    <p>The solution set is <m> \left\{ \left[\begin{array}{c}
-1 \\
-1 \\
0
\end{array}\right] \right\} </m>.</p>
  </answer>
</exercise>