1. Other
  2. Other
  3. let v be a real vector space a use the...

Question: let v be a real vector space a use the...

Question details

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 = \varnothing (That is, prove that we do not need to check this particular axiom for subsets of Vector Spaces.)

Solution by an expert tutor
Blurred Solution
This question has been solved
Subscribe to see this solution