How to determine if this is a vector space? need help! Thanks!

Let V = Real Number. Define α + β = 2α -β and c(α) = cα. For example, 3+5=2(3)-5=1 and 3(5)=15. Is V a vector space or not? Support your answer.

Re: How to determine if this is a vector space? need help! Thanks!

I think there was a similar post before. V is not a vector space under the operation defined here.

A vector space is an Abelian group under the addition operation defined. The above operation is not commutative.

For example : 3+5 = 1

5+3 = 2(5)-3 = 7