Can someone help me with solving a system of equations with 3 variables of varying matrix size?

This is a homework assignment that I have solved by hand by just doing one iteration, but I would love to know how to solve this using Matlab. I have spent hours trying to decipher how I would solve each iteration in Matlab. If someone can at the very least give me some insight on how to make this thing work that would be great. I'm trying to solve Problem III. Thanks.

[Walter Roberson]

Are you trying to numerically solve A * x = B for matrix A and B ? Or are the equations non-linear?

[Buckley Weglarz]

Non-linear. Kind of. I need to be able to run through every possible combination of R vs. Xr vs. theta in order to come up with unique values of V and X. The equations I'm using are in the PDF file I attached. I hope this makes it clear.