The problem with your code is sum = sum + i. Your i is defined as i = 1:b = 1:length(A). You are summing the index numbers of your column vector rather than the element of each row. In order words, no matter what element you define in your column vector, as long as the size is maintained (in your case, 3), you will always get the same answer 6. What you need to do is define sum = sum + A(i).
A=[1;2;3]; b=length(A);
sum=0; for i=1:b
sum= sum+A(i);
end
disp(sum)
