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

Problem:

\[
\begin{bmatrix} 
-2 & 2 & -2 & -2   \\ 
3 & -5 & -4 & -42   \\ 
0 & -3 & 1 & -10
\end{bmatrix}
\]

Solution:

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