Answer:

\[\operatorname{RREF} \left[\begin{array}{ccc|c} 3 & -2 & -2 & -15 \\ -2 & 1 & 0 & 8 \\ -1 & -3 & -1 & -4 \\ -1 & -1 & 1 & 2 \end{array}\right] = \left[\begin{array}{ccc|c} 1 & 0 & 0 & -3 \\ 0 & 1 & 0 & 2 \\ 0 & 0 & 1 & 1 \\ 0 & 0 & 0 & 0 \end{array}\right] \]

1. The vector equation \( x_{1} \left[\begin{array}{c} 3 \\ -2 \\ -1 \\ -1 \end{array}\right] + x_{2} \left[\begin{array}{c} -2 \\ 1 \\ -3 \\ -1 \end{array}\right] + x_{3} \left[\begin{array}{c} -2 \\ 0 \\ -1 \\ 1 \end{array}\right] = \left[\begin{array}{c} -15 \\ 8 \\ -4 \\ 2 \end{array}\right] \)has a solution.

2. \( \left[\begin{array}{c} -15 \\ 8 \\ -4 \\ 2 \end{array}\right] \) is a linear combination of the vectors \( \left[\begin{array}{c} 3 \\ -2 \\ -1 \\ -1 \end{array}\right] , \left[\begin{array}{c} -2 \\ 1 \\ -3 \\ -1 \end{array}\right] , \text{ and } \left[\begin{array}{c} -2 \\ 0 \\ -1 \\ 1 \end{array}\right] \).