Reduced Row Echelon Form: \[\begin{bmatrix} 1 & 0 & 0 & -1 \\ 0 & 1 & 0 & 5 \\ 0 & 0 & 1 & 2 \end{bmatrix}\] General Solution: \[ \begin{bmatrix} x_{ 1 } \\ x_{ 2 } \\ x_{ 3 } \\ \end{bmatrix} = \qquad \begin{bmatrix} -1 \\ 5 \\ 2 \end{bmatrix} \]

Problem:

\[
\begin{bmatrix} 
1 & 2 & -1 & 7   \\ 
-1 & -3 & 4 & -6   \\ 
2 & -5 & -2 & -31
\end{bmatrix}
\]

Solution:

\begin{solution}
Reduced Row Echelon Form: 
\[\begin{bmatrix} 
1 & 0 & 0 & -1   \\ 
0 & 1 & 0 & 5   \\ 
0 & 0 & 1 & 2
\end{bmatrix}\]
General Solution:
\[
\begin{bmatrix}
x_{ 1 } \\
x_{ 2 } \\
x_{ 3 } \\
\end{bmatrix} = \qquad
\begin{bmatrix} 
-1   \\ 
5   \\ 
2
\end{bmatrix}\]

\end{solution}