Solve the System of Linear Equations Using the Inverse Matrix

Solve the system of linear equations
$\left\{ \begin{array} { l } 6 x _ { 1 } - 12 x _ { 2 } - 6 x _ { 3 } - 12 x _ { 4 } = 0 \\18 x _ { 1 } - 30 x _ { 2 } - 12 x _ { 3 } - 18 x _ { 4 } = - 3 \\12 x _ { 1 } - 30 x _ { 2 } - 12 x _ { 3 } - 30 x _ { 4 } = 2 \\- 6 x _ { 1 } + 24 x _ { 2 } + 24 x _ { 3 } + 66 x _ { 4 } = 0\end{array} \right.$
using the inverse matrix $\frac { 1 } { 6 } \left[ \begin{array} { c c c c } - 24 & 7 & 1 & - 2 \\ - 10 & 3 & 0 & - 1 \\ - 29 & 7 & 3 & - 2 \\ 12 & - 3 & - 1 & 1 \end{array} \right]$ .

A) $\left[ \begin{array} { l } x _ { 1 } \\ x _ { 2 } \\ x _ { 3 } \\ x _ { 4 } \end{array} \right] = \left[ \begin{array} { c } - \frac { 19 } { 6 } \\ - \frac { 3 } { 2 } \\ - \frac { 5 } { 2 } \\ \frac { 7 } { 6 } \end{array} \right]$
B) $\left[ \begin{array} { l } x _ { 1 } \\ x _ { 2 } \\ x _ { 3 } \\ x _ { 4 } \end{array} \right] = \left[ \begin{array} { c } - \frac { 7 } { 6 } \\ - \frac { 5 } { 6 } \\ \frac { 3 } { 2 } \\ - \frac { 3 } { 2 } \end{array} \right]$
C) $\left[ \begin{array} { l } x _ { 1 } \\ x _ { 2 } \\ x _ { 3 } \\ x _ { 4 } \end{array} \right] = \left[ \begin{array} { c } - \frac { 3 } { 2 } \\ - \frac { 19 } { 6 } \\ 0 \\ \frac { 7 } { 6 } \end{array} \right]$
D)
$\left[ \begin{array} { l } x _ { 1 } \\ x _ { 2 } \\ x _ { 3 } \\ x _ { 4 } \end{array} \right] = \left[ \begin{array} { c } - \frac { 1 } { 2 } \\ \frac { 1 } { 6 } \\ 0 \\ \frac { 1 } { 3 } \end{array} \right]$
E) $\left[ \begin{array} { l } x _ { 1 } \\ x _ { 2 } \\ x _ { 3 } \\ x _ { 4 } \end{array} \right] = \left[ \begin{array} { c } 0 \\ - \frac { 1 } { 6 } \\ 0 \\ - \frac { 1 } { 3 } \end{array} \right]$

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