Question

Let the system of linear equations
$4 x+\lambda y+2 z=0$
$2 x-y+z=0$
$\mu x +2 y +3 z =0, \lambda, \mu \in R$
has a non-trivial solution. Then which of the following is true?

• A. $\mu=6, \lambda \in R$
• B. $\lambda=2, \mu \in R$
• C. $\lambda=3, \mu \in R$
• D. $\mu=-6, \lambda \in R$

Answer 1

Answer: (A)

For non-trivial solution
$\begin{vmatrix}4 & \lambda & 2 \\ 2 & -1 & 1 \\ \mu & 2 & 3\end{vmatrix}=0$
$\Rightarrow 2 \mu-6 \lambda+\lambda \mu=12$
when $\mu=6, \quad 12-6 \lambda+6 \lambda=12$
which is satisfied by all $\lambda$