Question

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 + λz = 0 has a non-trivial solution, then the value of λ is

(A) λ = 0

(B) λ = 1

(C) λ = -1

(D) None of these

Answer 1

Answer is (A) λ = 0

As the given system of equations has a non-trivial solution,

When λ = 0 then determinants become skew-symmetric determinants of odd order, which is equal to zero. Thus, λ = 0.