solve a system of equations symbolically

Hello

I want to solve a system of equations symbolically. But I faced some problems. I was wondering if you could guide me on why MATLAB is incapable of the determination of the Z as a function of a1 and a2? And how can I find Z?

Thanks for your attention in advance.

Here is my code:

clc
clear 

syms a3 a2 a1
eqn=[a3-3*a2+10*a1==68,5*a3+6*a2+2*a1==31];
S= solve(eqn);
X=S.a1

X = 

Y=S.a2

Y = 

Z=S.a3

Unrecognized field name "a3".

Answer 1

[Paul]

It looks like there are two equations with three unknowns for which there are many solutions. So solve() gives the results for two of the variables in terms of the third, which you can set to an arbitray value. In this case, it chose to solve for a1 and a2 in terms of a3. But you can make it solve for any two in terms of the third, for example a2 and a3 in terms of a1

syms a3 a2 a1
eqn = [a3-3*a2+10*a1==68,5*a3+6*a2+2*a1==31];
S = solve(eqn,[a2 a3])

S = struct with fields:
    a2: (16*a1)/7 - 103/7
    a3: 167/7 - (22*a1)/7

Now pick an arbitrary value for a1, say sqrt(3), and show that the solution satisfies the eqn

subs(eqn,[a1 a2 a3],[sqrt(3) subs([S.a2 S.a3],a1,sqrt(3))])

ans = 

[Mahsa Babaee]

Dear @Paul

First of all, thank you for your helpful answer. Now I want to extend this solution for a system of equations that consist of 5 equations and 11 unknowns as mentioned later. the equations are:

And the unknowns are:

I have to determine in terms of the .

I used your guidance and wrote the following code:

syms S1 S2 S3 A1 A2 A3 B1 B2 B3 M21 M32
eqn=[A1*sinh(S1)+B1*sinh(S1)-B2==0, A2*sinh(S2)+B2*cosh(S2)-B3==0, A3*sinh(S3)+B3*cosh(S3)==0, A1*cosh(S1)+B1*sinh(S1)-A2*M21==0, A2*cosh(S2)+B2*sinh(S2)-A3*M32==0];
S= solve(eqn, [A2 A3 B1 B2 B3]) 

But I can not see results for .

Could you please guide me on how could I determine in terms of the .?

[Paul]

It seems like you did everything correct. Are you getting results different than shown as follows?

syms S1 S2 S3 A1 A2 A3 B1 B2 B3 M21 M32
eqn=[A1*sinh(S1)+B1*sinh(S1)-B2==0, A2*sinh(S2)+B2*cosh(S2)-B3==0, A3*sinh(S3)+B3*cosh(S3)==0, A1*cosh(S1)+B1*sinh(S1)-A2*M21==0, A2*cosh(S2)+B2*sinh(S2)-A3*M32==0];
S= solve(eqn, [A2 A3 B1 B2 B3]);
S.A2

ans = 

S.A3

ans = 

S.B1

ans = 

S.B2

ans = 

S.B3

ans = 

[Mahsa Babaee]

Thanks a million.

It works!