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3. in this problem let v be a real vector space...

# 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.)