3) Let V = {("), a,b ER'} (note R* = {r € R|r > 0} ). Define "addition" on V by C) + C) - G) Further, define "scalar multiplication for c eR by c () = (). Prove that V is a vector space over R by showing that the set is closed under all the scalar multiplication and vectors addition and that all the axioms pertaining to these operations hold.

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