JEE Main 2021 (Online) 3rd August Evening ShiftQuestion 1
Let $A=(a_{ij})$ be a $3\times3$ matrix, where $a_{ij}=7^{\max\{i,j\}}$. Then $\det A$ is equal to
Determinant
Solution
$A=\begin{pmatrix}7&49&343\\49&49&343\\343&343&343\end{pmatrix}$ ($a_{ij}=7^{\max(i,j)}$ with $a_{11}=7$, $a_{12}=a_{21}=a_{22}=49$, rest $343$). $R_3\to R_3-R_2$, then $R_2\to R_2-R_1$: rows $(7,49,343),(42,0,0),(294,294,0)$. Expand along row 2: $\det=-42\,(49\cdot0-343\cdot294)=42\cdot343\cdot294=4235364=6^2\cdot7^6$. Option (C).