Problem 3 Show that additive inverses in vector spaces are unique, i.e. for any given vector v in a vector space V, there exists a unique v* € V such that v+v* = v*+v = : Ογ. Hint: take any vector v EV and suppose v₁ and v2 are both additive inverses of v. Try to show that v₁ = v2. Desired takeaways: Learning to prove uniqueness of an object by showing equality of potential two candidate objects.

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