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Math Help - Subspace of a vector space

  1. #1
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    Lightbulb Subspace of a vector space

    hi

    i solved this one, but am getting an answer different from the one given in the text book.

    Let V= Vector space of real polynomials
    W= set of all polynomials with degree>=6 and the zero polynomial(included)

    Is W a subspace of V? My answer was no.

    for the following set, u+v will not belong to W for

    u= x^6 +2x^5 + 1 v= -x^6 +x^5 + 2

    Here both u and v belong to W but the sum of those is a polynomial of degree less than 6.

    The text book says W is a subspace of V.

    Am I overlooking something?
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  2. #2
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    Re: Subspace of a vector space

    You are correct: W is not a subspace of V.
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  3. #3
    MHF Contributor FernandoRevilla's Avatar
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    Re: Subspace of a vector space

    Quote Originally Posted by MAX09 View Post
    The text book says W is a subspace of V. Am I overlooking something?
    Perhaps there is a typo in the text book: \leq 6 instead of \geq 6 . Or maybe the typo is in the answer.
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