Reduced Row Echelon Form: \[\begin{bmatrix} 1 & 0 & -5 & -4 \\ 0 & 1 & -4 & 2 \\ 0 & 0 & 0 & 0 \end{bmatrix}\] Basis: \[ \begin{bmatrix} 5 \\ 4 \\ 1 \\ 0 \end{bmatrix}, \qquad \begin{bmatrix} 4 \\ -2 \\ 0 \\ 1 \end{bmatrix}, \qquad \]

Problem:

\[
\begin{bmatrix} 
3 & -2 & -7 & -16   \\ 
3 & 0 & -15 & -12   \\ 
-6 & -1 & 34 & 22
\end{bmatrix}
\]

Solution:

\begin{solution}
Reduced Row Echelon Form: 
\[\begin{bmatrix} 
1 & 0 & -5 & -4   \\ 
0 & 1 & -4 & 2   \\ 
0 & 0 & 0 & 0
\end{bmatrix}\]
Basis:
\[\begin{bmatrix} 
 5  \\ 
 4  \\ 
 1  \\ 
 0
\end{bmatrix}, \qquad
\begin{bmatrix} 
 4  \\ 
 -2  \\ 
 0  \\ 
 1
\end{bmatrix}, \qquad
\]
\end{solution}