I have to equations:

y = T*Cx*U and x = T*Cy*U where

x and y are scalar values that are known,

Cx and Cy are both 4x4 matrices that are known.

T is a 1x4 vector : T=[1 t t^2 t^3] where t is unknown and

U is a 4x1 vector : U=[1 u u^2 u^3]' where ' means transpose and u is unknown.

So basically I have two equations and two unknowns, t and u. I would like to figure out a way to represent the equation so that

the unknowns are a function of the knowns

so that t = f(x,y,Cx,Cy) and u = f(x,y,Cx,Cy) or T = f(x,y,Cx,Cy) and U = f(x,y,Cx,Cy).

I imagine that getting the final numerical solution might involve getting the roots of a cubic but I don't know how to get that far.

I've tried to figure out a way to substitute one equation into the other to eliminate one of the unknowns (i.e., U or T) but I get stuck because I'm not sure what to do about dividing by a vector (i.e., finding the inverse of a vector?).