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

  1. #1
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    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.
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  2. #2
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    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
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