Solving an N-port

I have an N-Port which I want to derive the equivalent Z matrix, where N = 2 is the number of ports in this instance. So, for example,

P = Z * U

Where P and U are 2x1 vectors and Z is a 2x2 matrix.

I've applied conditions for P and measured U for two different cases. Ex

case 1: P = [1; -1], resulting U = [u11; u21] case 2: P = [-1; 1], resulting U = [u12; u22]

Now I want to solve for what the Z matrix

Z = [Z11 Z12; Z21 Z22]

using my known values. In other words, I'd like to know how I can use matlab solve for the components of Z in terms of the components of U and P. (ie a symbolic solution not a numeric one) I'd also like to know how to expand this since I may have a number of ports.

Thanks for your help!