jee-main 2019 Q78

jee-main · India · session1_12jan_shift2 Not Maths
The set of all values of $\lambda$ for which the system of linear equations $$\begin{aligned} & x - 2 y - 2 z = \lambda x \\ & x + 2 y + z = \lambda y \\ & - x - y = \lambda z \end{aligned}$$ has a non-trivial solution :
(1) is an empty set
(2) contains more than two elements
(3) is a singleton
(4) contains exactly two elements
The set of all values of $\lambda$ for which the system of linear equations
$$\begin{aligned}
& x - 2 y - 2 z = \lambda x \\
& x + 2 y + z = \lambda y \\
& - x - y = \lambda z
\end{aligned}$$
has a non-trivial solution :\\
(1) is an empty set\\
(2) contains more than two elements\\
(3) is a singleton\\
(4) contains exactly two elements