<div class="checkit exercise" data-checkit-slug="E3" data-checkit-title="Solving linear systems" data-checkit-seed="0005">
  <div class="exercise-statement">
    <p>Show how to find the solution set for the following system of linear equations. <p class="math math-display">\[\begin{matrix}
 x_{1} &amp;  -  &amp; 3 \, x_{2} &amp;  +  &amp; 7 \, x_{3} &amp;  -  &amp; 4 \, x_{4} &amp; = &amp; 4 \\
 x_{1} &amp;  -  &amp; 2 \, x_{2} &amp;  +  &amp; 4 \, x_{3} &amp;  -  &amp; 3 \, x_{4} &amp; = &amp; 3 \\
 2 \, x_{1} &amp;  -  &amp; 4 \, x_{2} &amp;  +  &amp; 8 \, x_{3} &amp;  -  &amp; 6 \, x_{4} &amp; = &amp; 6 \\
 \end{matrix}\]</p></p>
  </div>
  <div class="exercise-answer">
    <p>
      <b>Answer:</b>
    </p>
    <p class="math math-display">\[\mathrm{RREF} \left[\begin{array}{cccc|c}
1 &amp; -3 &amp; 7 &amp; -4 &amp; 4 \\
1 &amp; -2 &amp; 4 &amp; -3 &amp; 3 \\
2 &amp; -4 &amp; 8 &amp; -6 &amp; 6
\end{array}\right]  =  \left[\begin{array}{cccc|c}
1 &amp; 0 &amp; -2 &amp; -1 &amp; 1 \\
0 &amp; 1 &amp; -3 &amp; 1 &amp; -1 \\
0 &amp; 0 &amp; 0 &amp; 0 &amp; 0
\end{array}\right] \]</p>
    <p>The solution set is <span class="math math-inline">\( \left\{ \left[\begin{array}{c}
2 \, a + b + 1 \\
3 \, a - b - 1 \\
a \\
b
\end{array}\right] \middle|\,a\text{\texttt{,}}b\in\mathbb{R}\right\} \)</span>.</p>
  </div>
</div>



Collaborative Calculation and Data Science

colby

sagemath

Product

Resources

Company