Let the system of linear equations 4x+λy+2z=0 2x−y+z=0 μ+2y+3z=0,λ,μ∈R
has a non-trivial solution. Then which of the following is true?
A
μ=6,λ∈R
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B
λ=2,μ∈R
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C
λ=3,μ∈R
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D
μ=−6,λ∈R
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Solution
The correct option is Aμ=6,λ∈R For non-trivial solution Δ=0⇒∣∣
∣∣4λ22−11μ23∣∣
∣∣=0⇒4(−5)−λ(6−μ)+2(4+μ)=0⇒−12−6λ+λμ+2μ=0⇒−6(λ+2)+μ(λ+2)=0⇒(λ+2)(μ−6)=0⇒λ=−2 or μ=6
When λ=−2, first and second equation becomes same, so μ=6,λ∈R