JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
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 & Solution
Correct Answer
(A) \(\mu=6, \lambda \in R\)
Step-by-step Solution
Detailed explanation
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 \(\lambda\)
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