Solve the System of Linear Equations $\left\{ \begin{array} { l l } 7 x + 7 y + 7 z & = 0 \\21 x + 35 y + 28 z & = 6 \\21 x + 42 y + 35 z & = 1\end{array} \right.$

Multiple Choice

Solve the system of linear equations $\left\{ \begin{array} { l l } 7 x + 7 y + 7 z & = 0 \\21 x + 35 y + 28 z & = 6 \\21 x + 42 y + 35 z & = 1\end{array} \right.$ using the inverse matrix $\frac { 1 } { 7 } \left[ \begin{array} { c c c } 1 & 1 & - 1 \\- 3 & 2 & - 1 \\3 & - 3 & 2\end{array} \right]$ .

A) $\left[ \begin{array} { l } x \\y \\z\end{array} \right] = \left[ \begin{array} { c } \frac { - 5 } { 7 } \\\frac { 11 } { 7 } \\\frac { - 12 } { 7 }\end{array} \right]$
B) $\left[ \begin{array} { l } x \\y \\z\end{array} \right] = \left[ \begin{array} { c } \frac { 5 } { 7 } \\\frac { 11 } { 7 } \\\frac { - 16 } { 7 }\end{array} \right]$
C) $\left[ \begin{array} { l } x \\y \\z\end{array} \right] = \left[ \begin{array} { c } \frac { 16 } { 7 } \\\frac { 5 } { 7 } \\\frac { 11 } { 7 }\end{array} \right]$
D) $\left[ \begin{array} { l } x \\y \\z\end{array} \right] = \left[ \begin{array} { c } \frac { - 12 } { 7 } \\\frac { 11 } { 7 } \\\frac { - 5 } { 7 }\end{array} \right]$
E) $\left[ \begin{array} { l } x \\y \\z\end{array} \right] = \left[ \begin{array} { c } \frac { - 5 } { 7 } \\\frac { - 16 } { 7 } \\\frac { 11 } { 7 }\end{array} \right]$