Question

If the system of equations ax + y + z = 0, x + by + z = 0 and x + y + cz = 0 (a, b, c ≠ 1) has a non-trivial solution, then the value of 1/(1 - a) + 1/(1 - b) + 1/(1 - c) is

(A) -1

(B) 0

(C) 1

 (D) None of these

Answer 1

Answer is (C) 1

If given homogeneous system has non-trivial solution then C₁ - C₂, C₂ - C₃

Expanding along R₁ we get

(a - 1)[(b - 1)c - (1 - c)] + (1 - b)(1 - c) = 0

⇒ (1 - a)(1 - b)c + (1- a)(1 - c) + (1 - b)(1 - c) = 0 

Dividing by (1 - a)(1 - b)(1 - c), we get