Help with applying the least squares method for solving simultaneous equations

[yasith]

Hi everyone given the system of equations

A1Cx + B1Cy + C1Cz = D1
A2Cx + B2Cy + C2Cz = D2
A3Cx + B3Cy + C3Cz = D3

I need to solve for Cx, Cy, Cz
All other variables are known and constants.
However all other variables (A,b,c,d) come from experimentally measured data and thus I cannot use RREF to derive a unique solution.

This system will only have an approximate solution. Please help me with the strategy for solving these equations.

Yasith

 

[haruspex]

You have 3 equations and 3 unknowns. In the absence of any further information, and assuming there's no redundancy in the set of equations, there will be a unique, exact solution. I see no basis for allowing for experimental error.
If you had more equations then there's a standard technique, and it sounds like you're aware of that.