Reduced Row Echelon Form: \[\begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 3 & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix}\] Basis: \[ \begin{bmatrix} 0 \\ -3 \\ 1 \\ 0 \end{bmatrix}, \qquad \]

Problem:

\[
\begin{bmatrix} 
-1 & -5 & -15 & 2   \\ 
-1 & -3 & -9 & 2   \\ 
-5 & 4 & 12 & 2
\end{bmatrix}
\]

Solution:

\begin{solution}
Reduced Row Echelon Form: 
\[\begin{bmatrix} 
1 & 0 & 0 & 0   \\ 
0 & 1 & 3 & 0   \\ 
0 & 0 & 0 & 1
\end{bmatrix}\]
Basis:
\[\begin{bmatrix} 
 0  \\ 
 -3  \\ 
 1  \\ 
 0
\end{bmatrix}, \qquad
\]
\end{solution}