The set of all values of

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.

  1. contains more than two elements

  2. is a singleton

  3. is an empty set

  4. contains exactly two elements


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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