The system of linear equations
\begin{align*}
x + \lambda y - z &= 0\\
\lambda x - y - z &= 0\\
x + y - \lambda z &= 0
\end{align*}
has a non-trivial solution for:
(1) infinitely many values of $\lambda$
(2) exactly one value of $\lambda$
(3) exactly two values of $\lambda$
(4) exactly three values of $\lambda$