error with an assignment A(I) = B, the number of elements in B and I must be the same - matlab

Question

i have data set saved as .mat and i am trying to solve for a system of non-linear equations for unknown variables Ga and Ta. I'm using fsolve to solve it and the part of the relevant code is:
function F = msabase(x)
load ('matlab.mat');
Ta = x(1);
Ga = x(2);
util_a = exp(lamda.*(alpha_a - cost - w.*log(Ga)));
util_t = exp(lamda.*( - 2.5 - w.*log(2*0.80)));
F(1) = Ga - c0.*(1.+c1.*(Ta./cap).^c2).*d;
F(2) = Ta - sum.*(util_a/(util_a+util_t));
in each rows of the data set the values for all the other variables i.e lamda,alpha_a,cost, etc. are given. in line 7 of the code given, i'm getting the error "In an assignment A(I) = B, the number of elements in B and
I must be the same"
i'm not been able to understand why because it should be an element by element operation.

Answer 1

You are getting that error because you are trying to assign a vector / matrix of elements to a single slot in F. There is a dimension mismatch because you are trying to map more than one value into a single space in F, and that's ultimately why you are getting the error.
One suggestion I have is to either use cell arrays or create a 2D matrix that stores your values. If you prefer the cell array approach, each cell stores the desired calculation like so:
F = cell(2,1);
F{1} = Ga - c0.*(1.+c1.*(Ta./cap).^c2).*d;
F{2} = Ta - sum.*(util_a/(util_a+util_t));
Then to access the right slot, do either F{1} or F{2}. If you want the 2D matrix approach, you can concatenate both calculations into a single matrix by doing this:
F = [Ga - c0.*(1.+c1.*(Ta./cap).^c2).*d; Ta - sum.*(util_a/(util_a+util_t))];
This is assuming that each result is a single row vector, and so this will produce a 2D matrix where each row is the desired result. I'm not sure what size each computation is, and so to make things consistent, I'll make sure that both lines of code are row vectors:
F1 = Ga - c0.*(1.+c1.*(Ta./cap).^c2).*d;
F2 = Ta - sum.*(util_a/(util_a+util_t));
F = [F1(:).'; F2(:).'];

Answer 2

Try preallocating F before assignment. If you know that F is a 2-by-1 vector, insert F = zeros(2,1) somewhere before line 7. If you know nothing about the dimensions of F, initialise it as an empty matrix and append to it:
F = []
F = [F; (Ga - c0.*(1.+c1.*(Ta./cap).^c2).*d)];
F = [F; (Ta - sum.*(util_a/(util_a+util_t)))];
Beware that MATLAB is not particularly efficient at appending vectors/matrices, so preallocate if possible.