Use an Inverse Matrix to Find the Solution to the System

Multiple Choice

Use an inverse matrix to find the solution to the system.
- $$\left\{ \begin{aligned}x _ { 1 } + x _ { 3 } + x _ { 4 } & = 4 \\x _ { 2 } + x _ { 3 } - x _ { 4 } & = 12 \\2 x _ { 1 } + 2 x _ { 2 } + x _ { 3 } - 3 x _ { 4 } & = 23 \\4 x _ { 2 } + 2 x _ { 4 } & = 6\end{aligned} \right.$$

A) $x _ { 1 } = 1 , x _ { 2 } = 4 , x _ { 3 } = 0 , x _ { 4 } = 1$
B) no solution
C) $x _ { 1 } = 2 , x _ { 2 } = 2 , x _ { 3 } = - 5 , x _ { 4 } = - 6$
D) $x _ { 1 } = 1 , x _ { 2 } = 3 , x _ { 3 } = 6 , x _ { 4 } = - 3$