Solve returns empty result although solution exists

Hello I'm trying to solve the following system of equations,

This should be easy to solve by hand. However using solve returns an empty sym struct. what am i missing here?

variables used are attached.

Thank you.

EDIT: re-uploaded variables and added code.

EDIT2:provided working example as per @Walter Roberson's comment.

[Torsten]

But as far as I can see, there is nothing in your equations that must be treated symbolically.

Just use "\" to solve the linear system in p_ij.

[Star Strider]

Your .mat file fails. It is impossible to read its contents.

Post or attach your code as a text .m file, and attach your data in a readable form (.txt, .mat, or something else).

[Walter Roberson]

Is it possible that you have Maple installed on your system?

[Hazem Abdelghany]

yes I installed Maple specifically to see if it produces different outcome.

same problem occurred.

[Hazem Abdelghany]

@Torsten do you mean linsolve()?

Answer 1

[Walter Roberson]

You are accidentally using Maple's sym() and solve() calls. The .mat you provided for us is only useable by people who have installed "MATLAB Connector for Maple" .

You need to use pathtool to give the Maple functions a lower priority than the MATLAB functions and recreate the equations matrix and try again.

[Hazem Abdelghany]

Did as you said, you should be able to reproduce the error using Matlab's default symbolic toolbox now.

Thanks.

[Walter Roberson]

You have 15 equations in 14 variables and your system is inconsistent.

[Walter Roberson]

Part of the reason for inconsistency is your use of floating point numbers.

[A,b] = equationsToMatrix(eqns);
sol = A(1:14,:)\b(1:14);
A*sol-b

The final inconsistent row will be about 1E-13. A single bad round-off in your floating point values could lead to that.

[Hazem Abdelghany]

wow, thanks, finally some hope.

s there a way I can solve this? maybe some tolerance parameter?

i

[Walter Roberson]

The lines above show a solution in which the only inconsistency is on the order of 1E-13 , The order of the variables in sol will be the same as symvar(eqns)

Note: if you vpa(eqn) and compare that to your posted equations, you will see that they do not round exactly the same way. The equations in your .mat are not exactly the same as you would get by converting your posted equations to rationals. That matters because the correction you would need to make the equations consistent is less than the difference in stored versus posted values -- whatever round-off you have going in creating those coefficients is causing problems.