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Q.

A non trivial solution of the system of equations x+λy+2z=0,2x+λz=0,2λx2y+3z=0 is given by x:y:z=

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a

1 : - 2 : 2

b

2:1:2

c

1 : 2 : - 2

d

2:1:-2

answer is D.

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Detailed Solution

1    λ      22    0    λ2λ2    3=0 

1(2λ)-λ(6-2λ)+2(-4)=0λ32λ4=0(λ2)λ2+2λ+2=0

Taking λ=2 the system becomes  x+2y+2z=0 and 2x+0y+2z=0,4x-2y+3z=0

 x4=y2=z4x:y:z=2:1:2

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