a) let ???? = {(????, ????): ????, ???? ????}. define addition of elements of ???? coordinate

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Question:

a) let ???? = {(????, ????): ????, ???? ∈ ????}. define addition of elements of ???? coordinate wise, and for (????, ????) in ???? and ???? ∈ ????, define ????(????, ????) = { (????, ????) ???????? ???? = ???? (????????, ???? /???? ) ???????????? ≠ ???? is ???? a vector space over ???? with these operations? examine all the properties of vector space and justify your answer.