Question 42 - 2020 (04 Sep Shift 2)

Suppose the vectors $x_1, x_2$ and $x_3$ are the solutions of the system of linear equations, $Ax = b$ when the vector $b$ on the right side is equal to $b_1, b_2$ and $b_3$ respectively. If

$x_1 = \begin{bmatrix} 1 \ 1 \ 1 \end{bmatrix}$, $x_2 = \begin{bmatrix} 0 \ 2 \ 1 \end{bmatrix}$, $x_3 = \begin{bmatrix} 0 \ 0 \ 1 \end{bmatrix}$, $b_1 = \begin{bmatrix} 1 \ 0 \ 0 \end{bmatrix}$, $b_2 = \begin{bmatrix} 0 \ 2 \ 0 \end{bmatrix}$ and $b_3 = \begin{bmatrix} 0 \ 0 \ 2 \end{bmatrix}$, then the determinant of $A$ is equal to:

(1) $4$

(2) $2$

(3) $\dfrac{1}{2}$

(4) $\dfrac{3}{2}$