Suppose the vectors $x _ { 1 } , x _ { 2 }$ and $x _ { 3 }$ are the solutions of the system of linear equations, $A x = b$ when the vector $b$ on the right side is equal to $b _ { 1 } , b _ { 2 }$ and $b _ { 3 }$ respectively. If $x _ { 1 } = \left[ \begin{array} { l } 1 \\ 1 \\ 1 \end{array} \right] , x _ { 2 } = \left[ \begin{array} { l } 0 \\ 2 \\ 1 \end{array} \right] , x _ { 3 } = \left[ \begin{array} { l } 0 \\ 0 \\ 1 \end{array} \right] ; b _ { 1 } = \left[ \begin{array} { l } 1 \\ 0 \\ 0 \end{array} \right] , b _ { 2 } = \left[ \begin{array} { l } 0 \\ 2 \\ 0 \end{array} \right] , b _ { 3 } = \left[ \begin{array} { l } 0 \\ 0 \\ 2 \end{array} \right]$, then the determinant of $A$ is equal to\\
(1) 4\\
(2) 2\\
(3) $\frac { 1 } { 2 }$\\
(4) $\frac { 3 } { 2 }$