If the system of equations λx+(b−a)y+(c−a)z=0,  (a−b)x+λy+(c−b)z=0  and (a−c)x+(b−c)y+λx=0  has a non-trivial solutions, then the value of λ  is

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.