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?
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 $\lambda$
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.