Originally Posted by

**tusenfem**
You probably want to say that **x** is a function f(V1, V2, V3), and I have no idea why you put in A and B.

and you can have (0,0,2) or (0,3,0), also solutions of the equation that you are looking at.

No, it does not *require* two solutions, there are (at least) 2 solutions, like there were (at least) 3 solutions to the equation equal to 6.

If you want to discuss math, then you better do it correctly, you seem, like in your "philosophical discussions" just to put down what you like, whether founded in science or not. You actually have to *explain* what you want to do, and that means state at the beginning that you want to find all possible solutions to your equal 6 equation. If you don't say that, then we just have to guess, why you only come up with one solution (when there are clearly more) and why you suddenly are interested in the equal 0 equation. It is all in the clear explanations.

Are you sure about the linear dependancy? Methinks you don't know what linear dependency is if you claim that the two solutions are not linearly independent, or it may be a typo???? In a simple way it is that if you find solutions P, Q and R of your equal zero equation, then these solutions are linearly independent when you cannot write that cP + dQ = eR with c,d,e elements of N.

What you wrote down is a simple way of getting the whole set of solutions, so please write the text correctly, think a bit about what you want to present, read if it is correct or not.

No, not in a matrix, what *is* a matrix exactly?

You have here a vector equation giving you a 3D subset of 3D space that describe all points for the equal 6 equation.

first bold: read what you write before posting it!

second bold: prove it.