JEE Main 2021 (Online) 17th March Morning ShiftQuestion 1
The system of equations $kx+y+z=1$, $x+ky+z=k$ and $x+y+zk=k^{2}$ has no solution if $k$ is equal to :
Determinant
Solution
$\Delta=(k-1)^2(k+2)$. $k=1$: all three equations are $x+y+z=1$, consistent (infinite solutions). $k=-2$: rank of coefficients is 2 and the augmented rank is 3, so no solution. Option (D).