Question

If a system of equations
\[ a x + y + z = 0, \quad x - b y + z = 0, \quad x + y - c z = 0 \quad (a, b, c \ne -1) \]
has a non-zero solution, then
\[ \frac{1}{1+a} + \frac{1}{1+b} + \frac{1}{1+c} = \]

• A. 0
• B. 1
• C. 2
• D. 3

Hint:

Non-zero solution ⟹ determinant =0.

Answer 1

The Correct Option is B

For non-trivial solution, determinant of coefficients must be zero. Solving the determinant condition gives: 

(1)/(1+a)+(1)/(1+b)+(1)/(1+c)=1.