Apply Gaussian Elimination to Systems Without Unique Solutions
Use Gaussian $$\begin{array} { r } x + y + z + w = 8 \\3 x + 2 y + z + 4 w = 21 \\4 x + 4 y + 5 z + 8 w = 30 \\2 x + 3 y + 6 z + 9 w = 15\end{array}$$

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.
- $$\begin{array} { r } x + y + z + w = 8 \\3 x + 2 y + z + 4 w = 21 \\4 x + 4 y + 5 z + 8 w = 30 \\2 x + 3 y + 6 z + 9 w = 15\end{array}$$

A) $\{ ( - 6 w + 3,9 w + 7 , - 4 w - 2 , w ) \}$
B) $\{ ( 5 w + 11 , - 3 w - 7 , - 3 w + 4 , w ) \}$
C) $\{ ( - 3,16 , - 6,1 ) \}$
D) $\varnothing$