Solve the System of Equations $\left\{ \begin{array} { r } x + 3 y - 2 z = 1 \\2 x + 4 y + z = - 4 \\2 x + 6 y - z = 2\end{array} \right.$

Solve the system of equations $\left\{ \begin{array} { r } x + 3 y - 2 z = 1 \\2 x + 4 y + z = - 4 \\2 x + 6 y - z = 2\end{array} \right.$ by converting to a matrix equation and using its inverse coefficient matrix $\left[ \begin{array} { c c c } \frac { 5 } { 3 } & \frac { 3 } { 2 } & - \frac { 11 } { 6 } \\\\- \frac { 2 } { 3 } & - \frac { 1 } { 2 } & \frac { 5 } { 6 } \\\\- \frac { 2 } { 3 } & 0 & \frac { 1 } { 3 }\end{array} \right]$ .