\begin{exercise}{E3}{Solving linear systems}{0007}
\begin{exerciseStatement}
Show how to find the solution set for the following system of linear equations. \[\begin{matrix}
-2 \, x_{1} & + & x_{2} & - & 4 \, x_{3} & = & 3 \\
-3 \, x_{1} & - & 2 \, x_{2} & - & 7 \, x_{3} & = & -3 \\
& & x_{2} & & & = & 4 \\
x_{1} & & & + & 2 \, x_{3} & = & 0 \\
\end{matrix}\]
\end{exerciseStatement}
\begin{exerciseAnswer}\[\mathrm{RREF} \left[\begin{array}{ccc|c}
-2 & 1 & -4 & 3 \\
-3 & -2 & -7 & -3 \\
0 & 1 & 0 & 4 \\
1 & 0 & 2 & 0
\end{array}\right] = \left[\begin{array}{ccc|c}
1 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 \\
0 & 0 & 1 & 0 \\
0 & 0 & 0 & 1
\end{array}\right] \]
The solution set is \( \left\{\right\} \).
\end{exerciseAnswer}
\end{exercise}
