Apply Gaussian Elimination to Systems with More Variables Than Equations $$\begin{aligned}2 x + y + 2 z - 4 w & = 10 \\x + 3 y + 2 z - 11 w & = 17 \\3 x + y + 7 z - 21 w & = 0\end{aligned}$$

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.
- $$\begin{aligned}2 x + y + 2 z - 4 w & = 10 \\x + 3 y + 2 z - 11 w & = 17 \\3 x + y + 7 z - 21 w & = 0\end{aligned}$$

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