# Thread: Vector Space Axiom Proof

1. ## Vector Space Axiom Proof

Hello,

Is this right? I know this is trickier than it looks because you are only allowed to assume the axioms of vector spaces alone, nothing else.

2. Originally Posted by james121515
Hello,

Is this right? I know this is trickier than it looks because you are only allowed to assume the axioms of vector spaces alone, nothing else.

It is right but, imo, ugly. I prefer the following (be sure you can write down the axiom on which each step relies):

$c\cdot 0=c(0+0)=c\cdot 0+c\cdot 0\Longrightarrow c\cdot 0+(-c\cdot 0)=c\cdot 0+c\cdot 0+(-c\cdot 0) \Longrightarrow 0 = c\cdot 0 +0=c\cdot 0$ QED.

Tonio

3. only one quibble, tonio....i believe you should have written -(c0) rather than (-c)0.

yes, these are in point of fact equal, but proving that uses the fact that 0v = 0, for any v, which is somewhat of a detour.

(it's just a misplaced parenthesis, i'm sure you meant -(c0)).