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Math Help - subspaces

  1. #1
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    subspaces

    Give an example of a nonempty subset of U of R^2 st U is closed under scalar multiplication but U is not a subspace of R^2.



    so its ovbiously open under addition, so if I add another vertor in R^2, U+v will not be in R^2.

    not sure what this would be.
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  2. #2
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    Quote Originally Posted by CarmineCortez View Post
    Give an example of a nonempty subset of U of R^2 st U is closed under scalar multiplication but U is not a subspace of R^2.



    so its ovbiously open under addition, so if I add another vertor in R^2, U+v will not be in R^2.

    not sure what this would be.
    "U+v" makes no sense until you have specified what U is- and that's what the problem asks you to do!

    Let A be the subspace spanned by <1, 0> and B the subspace spanned by <0, 1>. What is the union of those two subspaces? Can you prove that U= A\cup B is closed under scalar multiplication but NOT under addition?
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  3. #3
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    subspaces and spans

    U is a subspace of the set of all polynomials P, it contains all polynomials of the form p=az^2+bz^2. Find the subspace W of P st P = U+W

    U+W is the span of P, not sure how to represent it.




    I meant to make a new thread.
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  4. #4
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    Quote Originally Posted by CarmineCortez View Post
    U is a subspace of the set of all polynomials P, it contains all polynomials of the form p=az^2+bz^2. Find the subspace W of P st P = U+W

    U+W is the span of P, not sure how to represent it.




    I meant to make a new thread.
    Are you sure about "p= az^2+ bz^2"? That is no different from "all polynomials of the form p= az^2".
    (And is not a subspace- it does not contain the 0 "vector". You probably meant "all polynomials of the form p= az^2+ bz+ c".)
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