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Question

The system of linear equations
x+λyz=0; λxyz=1; x+yλz=0 has a non - trivial solution for

A
infinitely many values of λ
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B
exactly one value of λ
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C
exactly two values of λ
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D
exactly three values of λ
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Solution

The correct option is D exactly three values of λ
Given, system of linear equation is
x+λyz=0; λxyz=0; x+yλz=0
Note that, given system will have a non - trivial solution only if determinant of coefficient matrix is zero,
i.e. ∣ ∣1λ1λ1111λ∣ ∣=0
1(λ+1)λ(λ2+1)1(λ+1)=0 λ+1+λ3λλ1=0 λ3λ=0(λ21)=0 λ=0 or λ=±1
Hence, given system of linear equation has a non - trivial solution for exactly three values of λ

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