JEE Main 2020 (Online) 4th September Evening ShiftQuestion 1
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 :
Determinant
Solution
$X=[x_1\,x_2\,x_3]$, $B=[b_1\,b_2\,b_3]$ satisfy $AX=B$. $\det B=1\cdot2\cdot2=4$ (diagonal), $\det X=\begin{vmatrix}1&0&0\\1&2&0\\1&1&1\end{vmatrix}=2$. $\det A=\det B/\det X=2$. Option (B).