vector Space

A vector Space over set for example : is a set closed number addition and scalar mutiplication satisfying the following axioms:

let ={(x,y):(x,y) } , and , , and .Then

(i)

(ii)

(iii)

(iv)for each

(v)for each

(vi)for each and each pair

(vii)for each pair of and each

(viii)for each pair of and each vector Span Bases linear Independence