JEE Main 2016 · 3 Apr · Shift 1 · Mathematics Q65

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The system of linear equations
$x+\lambda y-z=0$
$\lambda x-y-z=0$
$x+y-\lambda z=0$
has a non-trivial solution for :

infinitely many values of λ.

exactly one value of λ.

exactly two values of λ.

exactly three values of λ.

Answer and worked solution

Official answer: D

Non-trivial solutions need
$\begin{vmatrix}1&\lambda&-1\\\lambda&-1&-1\\1&1&-\lambda\end{vmatrix}=\lambda^3-\lambda=0,$
so λ = 0, 1 or −1: exactly three values.

Topics:Systems of linear equations

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JEE Main 2016 · 3 Apr · Shift 1, Mathematics question 65