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Questions  

If the system of equations λx+(ba)y+(ca)z=0,  (ab)x+λy+(cb)z=0  and (ac)x+(bc)y+λx=0  has a non-trivial solutions, then the value of λ  is

a
λ=0
b
λ=1
c
λ=−1
d
None of these

detailed solution

Correct option is A

As the given system of equations has non-trivial ⇒        |λ              b−a         c−aa−b          λ             c−ba−c       b−c            λ|=0 Whenλ=0,  then determinant becomes skew-symmetric determinants of odd order, which is equal to zero. Thus, λ=0.

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