How do you solve this type of equation?
a *X + b * Y + c *Z = q
d *X + e * Y + f *Z = w
X *X + Y * Y + Z *Z = z
We are looking for X,Y,Z. If not the squares in the last row this could be solved as a typical linear equation, for example using Linear Equations from Dot Numerics, or writing Gauss Elimination.
But how do I solve this one? Also, do you know any libraries in .NET that solves that equation?