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

Problem:

\[
\begin{bmatrix} 
-6 & -3 & 27 & 33   \\ 
-8 & -5 & 41 & 45   \\ 
-4 & 4 & -12 & 16
\end{bmatrix}
\]

Solution:

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

\end{solution}