Reduced Row Echelon Form: \[\begin{bmatrix} 1 & 0 & 3 & 1 \\ 0 & 1 & 0 & -5 \\ 0 & 0 & 0 & 0 \end{bmatrix}\] General Solution: \[ \begin{bmatrix} x_{ 1 } \\ x_{ 2 } \\ x_{ 3 } \\ \end{bmatrix} = \qquad \begin{bmatrix} 1 \\ -5 \\ 0 \end{bmatrix} \qquad + x_3 \begin{bmatrix} -3 \\ 0 \\ 1 \end{bmatrix} \]

Problem:

\[
\begin{bmatrix} 
-7 & -1 & -21 & -2   \\ 
0 & 1 & 0 & -5   \\ 
3 & 6 & 9 & -27
\end{bmatrix}
\]

Solution:

\begin{solution}
Reduced Row Echelon Form: 
\[\begin{bmatrix} 
1 & 0 & 3 & 1   \\ 
0 & 1 & 0 & -5   \\ 
0 & 0 & 0 & 0
\end{bmatrix}\]
General Solution:
\[
\begin{bmatrix}
x_{ 1 } \\
x_{ 2 } \\
x_{ 3 } \\
\end{bmatrix} = \qquad
\begin{bmatrix} 
1   \\ 
-5   \\ 
0
\end{bmatrix} \qquad +
x_3 \begin{bmatrix} 
 -3  \\ 
 0  \\ 
 1
\end{bmatrix}
\]

\end{solution}