Linear Algebra, one theoretic question

I've created geometric solver which solves geometric constraints (distance,angle,onplane,parralel and so on) applied on points in 3D space. Everything works fine but when I apply constraints on a point (one by one), I want to know when point becomes fully constrained. Of course I can drag point (not in mathcad) to find out this but it's not a math way.

So, how to find out that point becomes fully constrained after applying a few constraints?