a) Is the set U a vector space over with the above operations? Carefully justify your answer by checking each vector space axiom. If an axiom holds, give a proof; otherwise, explain why the axiom fails.

b)Is the set U as subspace of 2 ? Fully justify your answer.

Consider the following set U, where addition and scalar multiplication are de- fined as follows: U = {[2] 6 1R2 : 321,232 > 0} [:1 + [3:] = [2:21)] a. [2] 2 \":31 a) Is the set U a vector space over R with the above operations? Carefully justify your answer by checking each vector space axiom. If an axiom holds, give a proof; otherwise, explain why the axiom fails. b) Is the set U as subspace of R2? Fully justify your