\begin{exercise}{E3}{Solving linear systems}{0003}
\begin{exerciseStatement}
Show how to find the solution set for the following system of linear equations. \[\begin{matrix}
x_{1} & - & x_{2} & - & x_{3} & = & -6 \\
& & x_{2} & - & 3 \, x_{3} & = & 4 \\
& & & & 0 & = & 1 \\
& & 2 \, x_{2} & - & 6 \, x_{3} & = & 7 \\
\end{matrix}\]
\end{exerciseStatement}
\begin{exerciseAnswer}\[\mathrm{RREF} \left[\begin{array}{ccc|c}
1 & -1 & -1 & -6 \\
0 & 1 & -3 & 4 \\
0 & 0 & 0 & 1 \\
0 & 2 & -6 & 7
\end{array}\right] = \left[\begin{array}{ccc|c}
1 & 0 & -4 & 0 \\
0 & 1 & -3 & 0 \\
0 & 0 & 0 & 1 \\
0 & 0 & 0 & 0
\end{array}\right] \]
The solution set is \( \left\{\right\} \).
\end{exerciseAnswer}
\end{exercise}
