Question: let v be a real vector space a use the...
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 = (That is, prove that we do not need to check this particular axiom for subsets of Vector Spaces.)