Answer:

\[\operatorname{RREF} \left[\begin{array}{ccc|c} 3 & 0 & 4 & -2 \\ 2 & 1 & -3 & -6 \\ -5 & -3 & -3 & -6 \\ -3 & 1 & 0 & -4 \end{array}\right] = \left[\begin{array}{ccc|c} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right] \]

1. The vector equation \( x_{1} \left[\begin{array}{c} 3 \\ 2 \\ -5 \\ -3 \end{array}\right] + x_{2} \left[\begin{array}{c} 0 \\ 1 \\ -3 \\ 1 \end{array}\right] + x_{3} \left[\begin{array}{c} 4 \\ -3 \\ -3 \\ 0 \end{array}\right] = \left[\begin{array}{c} -2 \\ -6 \\ -6 \\ -4 \end{array}\right] \)has a solution.

2. \( \left[\begin{array}{c} -2 \\ -6 \\ -6 \\ -4 \end{array}\right] \) is not a linear combination of the vectors \( \left[\begin{array}{c} 3 \\ 2 \\ -5 \\ -3 \end{array}\right] , \left[\begin{array}{c} 0 \\ 1 \\ -3 \\ 1 \end{array}\right] , \text{ and } \left[\begin{array}{c} 4 \\ -3 \\ -3 \\ 0 \end{array}\right] \).