QJEEM16Ma979f: JEE Main 2016 Mathematics - Class 12 JEEM16Ma979f Solution: The system of linear equations x + λ y − z = 0 λ x − y − z = 0…

Question

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The system of linear equations

$\begin{matrix} x + λ y - z = 0 \\ λ x - y - z = 0 \\ x + y - λ z = 0 \end{matrix}$

has a non-trivial solution for :

Accepted Answer

For non-trivial solution, we have

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

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

$\Rightarrow λ (λ^{2} - 1) = 0$

$\Rightarrow λ = - 1, 0, 1$

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