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,…

Suppose the vectors $\displaystyle x_1, x_2$ and $\displaystyle x_3$ are the solutions of the system of linear equations, $\displaystyle \mathrm{A} x=\mathrm{b}$ when the vector b on the right side is equal to $\displaystyle \mathrm{b}_1, \mathrm{~b}_2$ and $\displaystyle \mathrm{b}_3$ respectively. If $$x_1=\left[\begin{array}{l} 1 \\ 1 \\ 1 \end{array}\right], x_2=\left[\begin{array}{l} 0 \\ 2 \\ 1 \end{array}\right], x_3=\left[\begin{array}{l} 0 \\ 0 \\ 1 \end{array}\right], \mathrm{b}_1=\left[\begin{array}{l} 1 \\ 0 \\ 0 \end{array}\right], $$ $\displaystyle \mathrm{b}_2=\left[\begin{array}{l}0 \\ 2 \\ 0\end{array}\right]$ and $\displaystyle \mathrm{b}_3=\left[\begin{array}{l}0 \\ 0 \\ 2\end{array}\right]$, then the determinant of A is equal to :