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 :

Question

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 $\lambda .$

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