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

Question

$\begin{array}{1 1}\text{(1) infinitely many values of }\; \lambda \\ \text{(2) exactly one value of }\; \lambda \\ \text{(3) exactly two values of}\; \lambda\\ \text{(4) exactly three values of}\; \lambda \end{array} $