JEE MAIN - Mathematics (2016 (Offline) - No. 9)
The system of linear equations
$$\matrix{ {x + \lambda y - z = 0} \cr {\lambda x - y - z = 0} \cr {x + y - \lambda z = 0} \cr } $$
has a non-trivial solution for :infinitely many values of $$\lambda .$$
exactly one value of $$\lambda .$$
exactly two values of $$\lambda .$$
exactly three values of $$\lambda .$$
Explanation
For non-trivial solution, we have
$$\left| {\matrix{ 1 & \lambda & { - 1} \cr \lambda & { - 1} & { - 1} \cr 1 & 1 & { - \lambda } \cr } } \right| = 0$$
$$ \Rightarrow 1(\lambda + 1) - \lambda ( - {\lambda ^2} + 1) - 1(\lambda + 1) = 0$$
$$ \Rightarrow \lambda ({\lambda ^2} - 1) = 0$$
$$ \Rightarrow \lambda = - 1,0,1$$
Comments (0)
