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Math Help - Vector spaces

  1. #1
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    Question Vector spaces

    Is the set of all polynomials over R of degree 2 a vector space over R ?

    My book says, the answer is no. I can't understand why ? Isn't Pn (set of all polynomials with degree <= n with coefficients from F) a vector space over F .

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  2. #2
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    Re: Vector spaces

    Hint: the set of all polynomials of degree <= 2 is a vector space, but the set of all polynomials of degree exactly 2 is not.
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  3. #3
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    Re: Vector spaces

    Quote Originally Posted by mrmaaza123 View Post
    Is the set of all polynomials over R of degree 2 a vector space over R ?

    You posted "of degree 2" not of degree \le 2. which is it?
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  4. #4
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    Re: Vector spaces

    Oh! right, Thank you. I got it now.
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  5. #5
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    Re: Vector spaces

    degree 2 doesn't include 0 vector so its not a vedtor space. <=2 includes 0.

    Edit: also, degree 2 includes (0,0,1) but not (0,1,0) or (1,0,0)
    Last edited by Hartlw; March 29th 2013 at 11:30 AM.
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