Question:
Let the system of linear equations
$4 x+\lambda y+2 z=0$
$2 x-y+z=0$
$\mu \mathrm{x}+2 \mathrm{y}+3 \mathrm{z}=0, \lambda, \mu \in \mathrm{R}$
has a non-trivial solution. Then which of the following is true?
Correct Option: 1
Solution:
For non-trivial solution
$\left|\begin{array}{ccc}4 & \lambda & 2 \\ 2 & -1 & 1 \\ \mu & 2 & 3\end{array}\right|=0$
$\Rightarrow 2 \mu-6 \lambda+\lambda \mu=12$
when $\mu=6, \quad 12-6 \lambda+6 \lambda=12$
which is satisfied by all $\lambda$