Solving a linear set of unknown Vectors

[m26k9]

Hello,

I am trying to find a mathematical procedure for finding the solutions for a linear set of vector equations.

For example I have;

Ax + By = P (1)
Cx + Dy = Q (2)

Here, A,B,C,D,x and y are all Nx1 vectors. So I need to solve for two Nx1 vectors.
For a general linear equations like Ax=B -> x=A^-1.B, is there any standard procedure to solve for vectors of unknowns?

Thank you very much.

 

[CompuChip]

If A and x are column (?) vectors, then what is Ax? Is it the inner product?
Because in that case, you have two equations for 2N unknowns which will give you a heavily underdetermined system.