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

Problem:

\[
\begin{bmatrix} 
-5 & 5 & -1 & 4   \\ 
-1 & 1 & -3 & 0   \\ 
4 & -4 & -3 & 0
\end{bmatrix}
\]

Solution:

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