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Math Help - Show that B' is a basis

  1. #1
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    Show that B' is a basis

    Hello,

    I was wondering, is it sufficient to prove that B' is a basis if I showed that B' is linearly independent?

    Or do is there anything else I would have to do?
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  2. #2
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    It needs to be a spanning set also.
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  3. #3
    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by l flipboi l View Post
    I was wondering, is it sufficient to prove that B' is a basis if I showed that B' is linearly independent?
    If B'\subset V has n elements and \dim V=n , then

    B'\textrm{\;lin.\;indep.\;}\Rightarrow B' \textrm{\;basis\;of\;}V

    Regards.

    Fernando Revilla
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