Hello, I'm not sure my question makes any sense at all, but after a long time without success I need some help.
I'm trying to solve a system like this:
A.x + B.y = v1, Transpose(B).x + C.y = v2,
where A,B and C are matrices, v1 and v2 are known vectors and x, y are my unknown vectors.
I tried to manipulate the system by multiplying by the inverse matrices to get two independent equations of the form:
A'.x = v1' B'.y = v2'
but it turns out that A' and B' are singular, which is quite unexpected since I can see no reason why my problem shouldn't have a (unique) solution. Maybe the reason is that my problem is badly conditioned... I don't know.
My question is: Is there a general way to solve my original system?