How would I use fsolve for 3 unknowns and 3 equations?

I'm confused on how to use fsolve when solving for "TT, a_1, b_1" in my code. I'm trying to solve for each of these variables using the 3 equations that are supposed to be in a 3x1 matrix which is set equal to 'equations.' Any help is much appreciated.

clear;clc;format long;

lm1=0; %m
lm2=-0.2; %m
Am=95; %m^2
At=3; %m^2
omega_m=40.2; %1/s
omega_t=228; %1/s
p=1.225; %kg/m^3

w=32000; %N
hm=0.96; %m
lt=6.5; %m
ht=0.72; %m

equations=@(TT a_1 b_1) [lm1*w+hm*w*a_1-1/Qt*sqrt(TT^3/2*p*At)-1/Qm*sqrt(w^3/2*p*Am)*b_1);hm*w*b_1+(ht*TT)+(1/Qm)*sqrt(w^3/2*p*Am)*a_1;1/Qm*sqrt(w^3/2*p*Am)-lt*TT+lm1*w*b_1];
equationsans=fsolve(equations,[1,1,1]');

Invalid expression. Check for missing multiplication operator, missing or unbalanced delimiters, or other syntax error. To construct matrices, use brackets instead of parentheses.

Answer 1

[Star Strider]

Provide values for ‘Qt’ and ‘Qm’ and then solve it —

clear;clc;format long;

lm1=0; %m
lm2=-0.2; %m
Am=95; %m^2
At=3; %m^2
omega_m=40.2; %1/s
omega_t=228; %1/s
p=1.225; %kg/m^3

w=32000; %N
hm=0.96; %m
lt=6.5; %m
ht=0.72; %m

Qm = rand

Qm = 
   0.770819305637386

Qt = rand

Qt = 
   0.909584161538862

equations=@(TT, a_1, b_1) [(lm1*w+hm*w*a_1-1/Qt*sqrt(TT^3/2*p*At)-1/Qm*sqrt(w^3/2*p*Am)*b_1);hm*w*b_1+(ht*TT)+(1/Qm)*sqrt(w^3/2*p*Am)*a_1;1/Qm*sqrt(w^3/2*p*Am)-lt*TT+lm1*w*b_1];
equationsans=fsolve(@(b)equations(b(1),b(2),b(3)),[1,1,1]')

Solver stopped prematurely.

fsolve stopped because it exceeded the function evaluation limit,
options.MaxFunctionEvaluations = 3.000000e+02.

equationsans = 3×1

1.0e+06 * 4.838264690667167 0.000000090313456 -0.000279936800090

There was an unpaired parenthesis in the first row of the vector that I completed. That was throwing the error.

.

[David Magana]

Thank you! helped a lot

[Star Strider]

As always, my pleasure!