Let V be a set with operation + and let F be a field with the operations + and . (dot) . an algebric expression ((V,+),(F,+.), .) with the internal and external operations is called vector space if it is satisfies following axioms.
1. (V,+) be an abelian group.
2. (F,+,.) Be closer with respect to dot.
3. a(æ+ß) = aæ+aß for all a,b is in F and æ,ß in V.
In other words we can express it as below..
we can describe this
1. (V,+) be an abelian group i,e, it satisfies 5 charactiristic closure associate identity inverse and commutative /
1 α,β in V then α+β in V.
2 α,β,γ in V then (α+β)+γ= α+(β+γ)
3 α in V , then there are exist 0 st α+0 = α
4 if α in V then -α in V st α+(α) in V.
5 α,β in V then α+β =β+α
2. (F,+,.) Be closer with respect to dot. i,e,
a in F and α in V st aα in V.
* set of real no is a vector space .