JEE Main 2022 (Online) 25th June Evening ShiftQuestion 1
The system of equations
$-kx+3y-14z=25$
$-15x+4y-kz=3$
$-4x+y+3z=4$
is consistent for all $k$ in the set
Determinant
Solution
$D=-(k-11)(k+11)$. For $k\neq\pm11$ the system has a unique solution, hence is consistent. For $k=\pm11$ rank of coefficient matrix is 2 and rank of augmented matrix is 3, so inconsistent. Hence consistent for $k\in\mathbf R-\{-11,11\}$. Option (D).