3 and 4 .Determinants and Matrices
hard

माना रैखिक समीकरण निकाय $4 x +\lambda y +2 z =0$ ; $2 x - y + z =0$ ; $\mu x +2 y +3 z =0, \lambda, \mu \in R$ का एक अतुच्छ हल है। तो निम्न में से कौन सा सत्य है ?

A

$\mu=6, \lambda \in R$

B

$\lambda=2, \mu \in R$

C

$\lambda=3, \mu \in R$

D

$\mu=-6, \lambda \in R$

(JEE MAIN-2021)

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 $\lambda$

Standard 12
Mathematics

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