Use Matrices and Gauss-Jordan Elimination to Solve Systems
Solve the System

Multiple Choice

Use Matrices and Gauss-Jordan Elimination to Solve Systems
Solve the system of equations using matrices. Use Gauss-Jordan elimination.
- $$\begin{aligned}x + y - z + w & = - 5 \\3 x - y + 3 z - 2 w & = 7 \\- 2 x + 2 y + z - w & = 16 \\- x - 2 y - 3 z + 3 w & = - 22\end{aligned}$$

A) $\{ ( - 2,3,4 , - 2 ) \}$
B) $\left\{ \left( - 2 , - 3,5 , \frac { 1 } { 2 } \right) \right\}$
C) $\{ ( 2 , - 3 , - 4 , - 2 ) \}$
D) $\left\{ \left( \frac { 1 } { 2 } , - \frac { 1 } { 3 } , - \frac { 1 } { 4 } , - \frac { 1 } { 2 } \right) \right\}$