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 11−a+11−b+11−c  is

For given homogenous equations to have non-zero solution, |a111b111c|=0    |a111−ab−101−a0c−1|=0⇒  a(b−1)(c−1)−(1−a)(c−1)−(1−a)(b−1)=0Dividing by (1−a)(1−b)(1−c),  we get       a1−a+11−c+11−b=0⇒      11−a+11−b+11−c=1