Question

If a system of equations -ax+y+z=0, x-by+z=0, x+y-cz=0 (a,b,c\ne1) has a non-zero solution, then (1)/(1+a)+(1)/(1+b)+(1)/(1+c) is

• A. 0
• B. 1
• C. 2
• D. 3

Hint:

For symmetric systems, convert determinant condition into a symmetric identity.

Answer 1

The Correct Option is B

For a non-zero solution, determinant of coefficients must be zero. This gives: a+b+c+2=abc Using this identity: (1)/(1+a)+(1)/(1+b)+(1)/(1+c)=1