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The system of equations λx+y+z=0,     x+λy+z=0,   xy+λz=0 will have a non- trivial solution for  real values of λare

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a
0,1
b
0,-1
c
0,2
d
0

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detailed solution

Correct option is D

The condition for homogeneous system to have a non-trivial solution is Δ=0⇒λ11-1λ1-1-1λ=0⇒λλ2+1-[-λ+1]+[1+λ]=0⇒λ3+λ+λ-1+1+λ=0⇒λ3+3λ=0⇒λλ2+3=0⇒λ=0


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