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Suppose a,bR and a,b1. If the system of equations ax+y+z=0, x+by+z=0, x+y+2z=0 has a non-trivial solution then

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a
a+b=2ab
b
a+b=ab
c
a+1b=2
d
a+b=0

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detailed solution

Correct option is A

The condition for a homogeneous system of equations to have a non-zero solution is Δ=0⇒a111b1112=0⇒a(2b−1)−1(2−1)+1(1−b)=0⇒2ab−a−1+1−b=0⇒a+b=2ab


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