JEE Main 2019 (Online) 8th April Morning ShiftQuestion 1
The greatest value of $c\in R$ for which the system of linear equations $x-cy-cz=0$, $cx-y+cz=0$, $cx+cy-z=0$ has a non-trivial solution, is
Determinant
Solution
The determinant $\begin{vmatrix}1&-c&-c\\c&-1&c\\c&c&-1\end{vmatrix}=0$ factors as $(1+c)^2(1-2c)$ up to sign, so $c=-1$ or $\tfrac12$. The greatest is $\tfrac12$.