# Question: in this problem let v be a real vector space...

###### Question details

In this problem let V be a real vector space.

(a) Use the ten axioms to prove that the additive inverse of
**v** ∈ V is unique.

(b) Use the ten axioms to prove that the additive inverse of v ∈
V is given by the scalar multiplication of
(−1)**v**.

(c) Let S be a subset of a V. Prove that if S is closed under
addition and scalar multiplication, then for every
**v** ∈ S, there exists a **w** such that
**v** + **w** = 0. (That is, prove that
we do not need to check this particular axiom for subsets of Vector
Spaces.)