Apply Gaussian Elimination to Systems Without Unique Solutions
Use Gaussian $$\begin{array} { r } 3 x - 2 y + 2 z - w = 2 \\4 x + y + z + 6 w = 8 \\- 3 x + 2 y - 2 z + w = 5 \\5 x + 3 z - 2 w = 1\end{array}$$

Multiple Choice

Apply Gaussian Elimination to Systems Without Unique Solutions
Use Gaussian elimination to find the complete solution to the system of equations, or state that none exists.
- $$\begin{array} { r } 3 x - 2 y + 2 z - w = 2 \\4 x + y + z + 6 w = 8 \\- 3 x + 2 y - 2 z + w = 5 \\5 x + 3 z - 2 w = 1\end{array}$$

A) $\varnothing$
B) $\left\{ \left( 2,0 , - \frac { 3 } { 37 } , \frac { 9 } { 37 } \right) \right\}$
C) $\left\{ \left( \frac { 1 } { 2 } , 0 , - \frac { 37 } { 3 } , \frac { 37 } { 9 } \right) \right\}$
D) $\left\{ \left( 1 , - \frac { 1 } { 3 } , \frac { 4 } { 9 } , 6 \right) \right\}$