\begin{exercise}{E3}{Solving linear systems}{0001}
\begin{exerciseStatement}
Show how to find the solution set for the following system of linear equations. \[\begin{matrix}
x_{1} & & & - & x_{3} & = & 4 \\
x_{1} & + & x_{2} & & & = & 3 \\
x_{1} & + & x_{2} & + & x_{3} & = & -2 \\
& & & & x_{3} & = & -4 \\
\end{matrix}\]
\end{exerciseStatement}
\begin{exerciseAnswer}\[\mathrm{RREF} \left[\begin{array}{ccc|c}
1 & 0 & -1 & 4 \\
1 & 1 & 0 & 3 \\
1 & 1 & 1 & -2 \\
0 & 0 & 1 & -4
\end{array}\right] = \left[\begin{array}{ccc|c}
1 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 \\
0 & 0 & 1 & 0 \\
0 & 0 & 0 & 1
\end{array}\right] \]
The solution set is \( \left\{\right\} \).
\end{exerciseAnswer}
\end{exercise}
