[Solved] System of equations with for loop (3 variables and 10 equations)

Hello all :)

I am trying to solve a system of equations with for loop (3 variables and 3 equations, 10 times):

TSR=7.5;    %Tip Speed Ratio
k=2;
eps_design=0.0023;
x=linspace(1,TSR,10)';

%a, a', beta_i
syms a a_prime_for beta_i_for
a = zeros(size(x));
a_prime = zeros(size(x));
beta_i = zeros(size(x));
for i = 1:numel(x)
    eqn_1 = a_for/(1-a_for)==(F*cos(beta_i_for)*(1+eps_design*tan(beta_i_for)))/(8*pi*k*(sin(beta_i_for))^2);
    eqn_2 = a_prime_for/(1+a_prime_for)==(F*(1-eps_design*cot(beta_i_for)))/(8*pi*k*cos(beta_i_for));
    eqn_3 = tan(beta_i_for)==(1-a_for)/(x(i)*(1+a_prime_for));
    eqns=[eqn_1,eqn_2,eqn_3];
    S=double(vpasolve(eqns,[a_for a_prime_for beta_i_for]));
    [a(i),a_prime(i),beta_i(i)]=[S.a_for,S.a_prime_for,S.beta_i_for];
end

But I get this error, and I don't understand it:

This expression cannot be assigned to multiple values. (line  [a(i),a_prime(i),beta_i(i)]=[S.a_for,S.a_prime_for,S.beta_i_for];)

Error using sym.getEqnsVars>checkVariables (line 92)
Second argument must be a vector of symbolic variables.

Error in sym.getEqnsVars (line 54)
    checkVariables(vars);

Error in sym/vpasolve (line 132)
    [eqns,vars] = sym.getEqnsVars(varargin{1:N});

Error in Assigment1 (line 207)
    S=double(vpasolve(eqns,[a_for a_prime_for beta_i_for]));
    

Thank you in advance for your help :)

EDIT1: changed F in eqn_1 and eqn_2 to F(i). I had not the same number of equations between the left and right sides of those equations. But I still have an error now.

    Error using double
Conversion to double from struct is not possible.

Error in Assigment1 (line 207)
    S=double(vpasolve(eqns,[a_for a_prime_for beta_i_for]));
    

EDIT2: Okay, I took away the double function and it works now. :) Here is my final code:

% -B.3 Induction factors (a, a') and beta_i

F=(Z*c_radius*C_Ldesign)./(x./TSR); %Loading Force
k=2;

%a, a', beta_i
syms a_for a_prime_for beta_i_for
a = zeros(size(x));
a_prime = zeros(size(x));
beta_i = zeros(size(x));
for i = 1:numel(x)
    eqn_1 = a_for/(1-a_for)==(F(i)*cos(beta_i_for)*(1+eps_design*tan(beta_i_for)))/(8*pi*k*(sin(beta_i_for))^2);
    eqn_2 = a_prime_for/(1+a_prime_for)==(F(i)*(1-eps_design*cot(beta_i_for)))/(8*pi*k*cos(beta_i_for));
    eqn_3 = tan(beta_i_for)==(1-a_for)/(x(i)*(1+a_prime_for));
    eqns=[eqn_1,eqn_2,eqn_3];
    S=vpasolve(eqns,[a_for a_prime_for beta_i_for]);
    a(i)=S.a_for;
    a_prime(i)=S.a_prime_for;
    beta_i(i)=S.beta_i_for;
end

By the way, F was

F =

    3.3671
    1.5299
    0.8375
    0.5207
    0.3530
    0.2543
    0.1916
    0.1494
    0.1197
    0.0981

[Torsten]

syms a_for a_prime_for beta_i_for