JEE Main 2025 (Online) 23rd January Evening ShiftQuestion 1
Let $A=[a_{ij}]$ be a $3\times3$ matrix such that $A\begin{bmatrix}0\\1\\0\end{bmatrix}=\begin{bmatrix}0\\0\\1\end{bmatrix}$, $A\begin{bmatrix}4\\1\\3\end{bmatrix}=\begin{bmatrix}0\\1\\0\end{bmatrix}$ and $A\begin{bmatrix}2\\1\\2\end{bmatrix}=\begin{bmatrix}1\\0\\0\end{bmatrix}$, then $a_{23}$ equals :
Matrices
Solution
Write $AM=N$ with $M$ the matrix of the three input columns, $N$ the output columns. Then $A=NM^{-1}$, whose second row is $(1,0,-1)$, so $a_{23}=-1$.