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
$x=\left[\begin{array}{l}1 \\ 1 \\ 1\end{array}\right], x_{2}=\left[\begin{array}{l}0 \\ 2 \\ 1\end{array}\right], x_{3}=\left[\begin{array}{l}0 \\ 0 \\ 1\end{array}\right], b_{1}=\left[\begin{array}{l}1 \\ 0 \\ 0\end{array}\right]$
$\mathrm{b}_{2}=\left[\begin{array}{l}0 \\ 2 \\ 0\end{array}\right]$ and $\mathrm{b}_{3}=\left[\begin{array}{l}0 \\ 0 \\ 2\end{array}\right]$, then the determinant of
$\mathrm{A}$ is equal to :-
Correct Option: , 4
$\mathrm{Ax}_{1}=\mathrm{b}_{1}$
$\mathrm{Ax}_{2}=\mathrm{b}_{2}$
$\mathrm{Ax}_{3}=\mathrm{b}_{3}$
$\Rightarrow \quad|\mathrm{A}|\left|\begin{array}{lll}1 & 0 & 0 \\ 1 & 2 & 0 \\ 1 & 1 & 1\end{array}\right|=\left|\begin{array}{lll}1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2\end{array}\right|$
$\Rightarrow|\mathrm{A}|=\frac{4}{2}=2$