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?).