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Let the system of linear equations \(\begin{aligned}& 4 x+\lambda y+2 z=0 \\& 2 x-y+z=0 \\& \mu x+2 y+3 z=0, \lambda, \m…

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Let the system of linear equations
\(\begin{aligned}& 4 x+\lambda y+2 z=0 \\& 2 x-y+z=0 \\& \mu x+2 y+3 z=0, \lambda, \mu \in R\end{aligned}\)

has a non-trivial solution. Then which of the following is true?

[JEE Main 2021, 18 Mar (Shift 2)]

a

\(\mu=6, \lambda \in R\)

b

\(\mu=-6, \lambda \in R\)

c

\(\lambda=2, \mu \in R\)

d

\(\lambda=3, \mu \in R\)

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