Since Matlab stores values in a non-decimal representation, there is a lot of potential for round. In general you should be using a tolerance if you want to test equality for a non-integer data type. The required tolerance is an not really arbitrary choice, but depends on the context. If you expect an exact solution you should use something like 2*eps, while if you expect a non-exact solution you should use something that makes sense for you.
To get the exact answer you expected (2130), the precision needs to be a bit of an odd value. Also, a while loop makes more sense if you don't know how many iterations you need.
% constants:
R1 = 3000 ;
R2 = 8000 ;
R4 = 2000 ;
R5 = 4000 ;
% R3 = 2130 ; <--- this should be the answer for "r" below
v = 110 ;
solution_list=NaN(1,1000);%review the result for debugging
for r = 2000:3000
R3 = r;
A = [0 -R2 0 -R4 0 0 % the "A" matrix
R1 -R2 R3 0 0 0
0 0 -R3 -R4 R5 0
-1 -1 0 0 0 1
0 1 1 -1 0 0
1 0 -1 0 -1 0
0 0 0 1 1 -1];
b = [-v; 0; 0; 0; 0; 0; 0];
x = A\b ; % the answer column vector
solution_list(r-1999)=x(4);
if abs(x(4)-0.0170)<3.68*10^-6
answer = r
break
end
end
