Cell elements must be character arrays. (Solver equations created in a loop)

I am trying to solve a system of linear equations numerically, where I have 3 variables and 50 equations. I am creating the euations in a foor loop. here is my code:

Temps_all = [500, 550, 600, 650, 700];
Shear_cal = [0.019, 0.038, 0.058, 0.067, 0.077, 0.096, 0.115, 0.135, 0.154, 0.231];
syms ln_A delta_E delta_X
Yield = [2, 4, 12, 33, 57, 2, 6, 14, 30, 59, 2, 8, 15, 34, 59, 3, 5, ...
    11, 33, 55, 7, 8, 12, 44, 58, 6, 12, 32, 44, 58, 12, 15, 36, 58, ...
    68, 15, 21, 41, 58, 75, 7, 18, 42, 53, 69, 11, 23, 31, 48, 72, 3, ...
    4, 13, 40, 57];
Ar = 42;
kB = 0.001985875;
C = 6.941215543; % Convergence factor
eqns_all = [];
for shear = 1:length(Shear_cal)
    for temp = 1:length(Temps_all)
        eqn = ln_A -(delta_E-Ar*delta_X*Shear_cal(shear))*C/(kB*Temps_all(temp))...
            - log(Yield((shear-1)*length(Temps_all)+temp)) == 0;
        eqns_all = [eqns_all;{eqn}];
    end
end

S_all = solve(eqns_all,[ln_A delta_E delta_X]);

The euations are created and appended to the equation list eqns_all. But when I run the script I get the following error at the last line where solver is being used. I am not fimiliar with character arrays so any help is greatly appreciated.

Error using char

Cell elements must be character arrays.

Error in solve>isOption (line 459)

b = ~isa(a, 'logical') && any(strcmpi(char(a), ...

Error in solve>getEqns (line 392)

while k <= numel(argv) && ~isOption(argv{k})

Error in solve (line 226)

[eqns,vars,options] = getEqns(varargin{:});

Error in Bell (line 34)

S_all = solve(eqns_all,[ln_A delta_E delta_X]);

Answer 1

[Walter Roberson]

        eqns_all = [eqns_all;{eqn}];

solve() cannot process a cell array of equations. You should leave out the {}

[Karen Mohammadtabar]

Thank you that works, also changing ";" to "," helps with correcting the dimensions

Answer 2

[Surya Talluri]

I understand that you want to solve a system of 50 linear equations for 3 variables. I am not able to reproduce the error on my side.

If the error is persisting, you can try solving the linear equations using “equationsToMatrix” and “linsolve” functions.

[A, B] = equationsToMatrix(eqns_all, [ln_A delta_E delta_X]);

S_all = linsolve(A,B);

You can have a look at the documentation for further understanding - https://www.mathworks.com/help/symbolic/solve-a-system-of-linear-equations.html

[Karen Mohammadtabar]

Thank you but the error is solved by actually doing the following:

eqns_all = [eqns_all;{eqn}]; --> eqns_all = [eqns_all,eqn];