Question:
The set of all values of $\lambda$ for which the system of linear equations.
$x-2 y-2 z=\lambda x$
$x+2 y+z=\lambda y$
$-x-y=\lambda z$
has a non-trivial solution.
Correct Option: , 2
Solution:
$\left|\begin{array}{ccc}\lambda-1 & 2 & 2 \\ 1 & 2-\lambda & 1 \\ 1 & 1 & 1\end{array}\right|=0 \Rightarrow(\lambda-1)^{3}=0 \Rightarrow \lambda=1$
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