Suppose the vectors \( x_{1}, x_{2} \) and \( x_{3} \) are the solutions of the system of linear equations, \( \mathrm{A…

Suppose the vectors \( x_{1}, x_{2} \) and \( x_{3} \) are the solutions of the system of linear equations, \( \mathrm{Ax}=\mathrm{b} \) when the vector \( \mathrm{b} \) on the right side is equal to \( \mathrm{b}_{1}, \mathrm{~b}_{2} \) and \( \mathrm{b}_{3} \) respectively. If

\( \mathrm{x}_{1}=\left[\begin{array}{l}1 \\ 1 \\ 1\end{array}\right], \mathrm{x}_{2}=\left[\begin{array}{l}0 \\ 2 \\ 1\end{array}\right], \mathrm{x}_{3}=\left[\begin{array}{l}0 \\ 0 \\ 1\end{array}\right], \mathrm{b}_{1}=\left[\begin{array}{l}1 \\ 0 \\ 0\end{array}\right], \mathrm{b}_{2}=\left[\begin{array}{l}0 \\ 2 \\ 0\end{array}\right] \) and \( \mathrm{b}_{3} \) \( =\left[\begin{array}{l}0 \\ 0 \\ 2\end{array}\right] \), then the determinant of \( \mathrm{A} \) is equal to :

[JEE Main 2020, 4 Sep (Shift 2)]