Solve System of Equations for Mesh Circuit Analysis in S-Domain

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Ian Van Giesen on 21 Feb 2021
Edited: Ian Van Giesen on 23 Feb 2021
I am trying to solve for input voltage in terms of one current (I3 in my case). I've used KVL to derive the equations, but beyond that I'm a bit lost. I looked around at MATLAB Answers and haven't found anything. When I solve my system, I get the following response: Vi = Empty sym: 0-by-1. What does that even mean?
syms I1 I2 I3 I4 Vi s
eqn1 = (2*s)*I1 +(-s)*I2 +(-2)*I4 - Vi==0;
eqn2 = (-s)*I1 +(2*s+1)*I2 + (-1)*I3==0;
eqn3 = (-1)*I2 + ((2/s)+1)*I3 +(-1/s)*I4==0;
eqn4 = (-s)*I1 + (-1/s)*I3 + (s+1/s)*I4==0;
Vi = solve(eqn1, eqn2, eqn3, eqn4, I3)
I've inserted by code above for reference. If anyone can provide a little guidance, that would be great. Thank you.

Vimal Rathod on 23 Feb 2021
Hi,
The reason you are getting an empty value from the solve function is because it cannot find a solution for the given set of equations. You could probably add more equations to the set of equations by using KCL equations.
Ian Van Giesen on 23 Feb 2021
Ah, okay perhaps I should have clarified. I am looking for the symbolic algebraic solution to this system of linear equations in terms of two variable (s and I3). I solved the problem by hand but the process was very tedious (~4 pages). @Vimal Rathod thank you for the input!