If \(u,v \in V_{n}\) then \((u+v=v+u)\in V_{n}\) (commutative law)
If \(u,v,w \in V_{n}\) then \(u+(v+w)=(v+u)+w \in V_{n}\) (associative law)
There exists a unique vector 0 (zero or null vector) in \(V_{n}\) such that \(x+0=x\text{.}\) For any \(x\) in \(V_{n}\text{.}\) (Existance of a zero vector)
For each vector \(x\) in \(V_{n}\text{,}\) there exists a unique vector \(-x\) in \(V_{n}\) such that \(x+(-x)=0\text{.}\) (Existance of additive inverse)
