Solve the System of Linear Equations $\left\{ \begin{array} { l l } - 6 x + 18 y + 6 z & = 1 \\12 x + 30 y & = 2 \\18 x + 6 y - 12 z & = - 1\end{array} \right.$

Multiple Choice

Solve the system of linear equations $\left\{ \begin{array} { l l } - 6 x + 18 y + 6 z & = 1 \\12 x + 30 y & = 2 \\18 x + 6 y - 12 z & = - 1\end{array} \right.$ using an inverse matrix.

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