If the system of 3 equations
has a non-trivial solution, then 1/(1-a) + 1/(1-b) + 1/(1-c) = ?
The choices are 1, 2, 0 or -1
It seems obvious to me that if a=b=c=1, the system reduces to one equation and has a non-trivial solution. But infinity isn't among the options.
Oh, and there isnt any clause stating that a, b and c are distinct.
You have 3 equations in 3 unknowns. Geometrically, this means that the 3 planes coincide and that those values of x,y,z that satisfy the equation ax+b+z=0, automatically satisfy all three equations. Most of the times, a system with the same number of equations and unknowns has a single unique solution. By the way, we say that a linear system is homogeneous if its constant term is zero!
Originally Posted by nahduma
But what is the answer?
I understand that, but it still doesn't answer my question.