Reduced Row Echelon Form: \[\begin{bmatrix} 1 & 0 & 0 & -4 \\ 0 & 1 & 0 & 4 \\ 0 & 0 & 1 & -3 \end{bmatrix}\] Basis: \[ \begin{bmatrix} 4 \\ -4 \\ 3 \\ 1 \end{bmatrix}, \qquad \]

Problem:

\[
\begin{bmatrix} 
4 & 4 & 2 & -6   \\ 
-5 & -3 & -4 & 20   \\ 
0 & 0 & 4 & -12
\end{bmatrix}
\]

Solution:

\begin{solution}
Reduced Row Echelon Form: 
\[\begin{bmatrix} 
1 & 0 & 0 & -4   \\ 
0 & 1 & 0 & 4   \\ 
0 & 0 & 1 & -3
\end{bmatrix}\]
Basis:
\[\begin{bmatrix} 
 4  \\ 
 -4  \\ 
 3  \\ 
 1
\end{bmatrix}, \qquad
\]
\end{solution}