Use Matrices and Gaussian Elimination to Solve Systems
Solve the System

Use Matrices and Gaussian Elimination to Solve Systems
Solve the system of equations using matrices. Use Gaussian elimination with back-substitution.
- $$\begin{aligned}x + y + z - w & = 6 \\2 x - y + 3 z + 4 w & = - 4 \\4 x + 2 y - z - w & = - 13 \\- x - 2 y + 4 z + 3 w = & 12\end{aligned}$$

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