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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.