Apply Gaussian Elimination to Systems with More Variables Than Equations $$\begin{array} { r } 3 x + y + z - 2 w = 10 \\2 x + 3 y + 3 z + w = - 5 \\2 x + y + 4 z + 11 w = 11\end{array}$$

Multiple Choice

Apply Gaussian Elimination to Systems with More Variables than Equations
Use Gaussian elimination to find the complete solution to the system of equations, or state that none exists.
- $$\begin{array} { r } 3 x + y + z - 2 w = 10 \\2 x + 3 y + 3 z + w = - 5 \\2 x + y + 4 z + 11 w = 11\end{array}$$

A) $\{ ( w + 5,3 w - 7 , - 4 w + 2 , w ) \}$
B) $\{ ( 2 w + 3,6 w - 7 , - 10 w + 8 , w ) \}$
C) $\{ ( 6 , - 4 , - 2,1 ) \}$
D) $\{ ( 7 , - 1 , - 6,2 ) \}$