Q58 / 90 · JEE Main 2019 (12 Jan Shift 2) · Mathematics

The set of all values of $λ$ for which the system of linear equations
$x - 2 y - 2 z = λ x$
$x + 2 y + z = λ y$
$- x - y = λ z$
has a non-trivial solution :

Solution

For non-trivial solution, $∆ = 0$ .

$\Rightarrow |\begin{matrix} 1 - λ & - 2 & - 2 \\ 1 & 2 - λ & 1 \\ - 1 & - 1 & - λ \end{matrix}| = 0$

$\Rightarrow (1 - λ) (- 2 λ + λ^{2} + 1) + 1 (- λ + 1) - 1 (- 1 + 2 - λ) = 0$

$\Rightarrow λ^{2} - 3 λ^{2} + 3 λ - 1 = 0$

$\Rightarrow {(λ - 1)}^{3} = 0$

$\Rightarrow λ = 1$

Singleton set

Hence, the correct answer is option: 'C'.