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Math Help - Vector Subspaces

  1. #1
    Member Ranger SVO's Avatar
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    Vector Subspaces

    Its Spring Break so I've decided to get and stay caught up

    Determine if the given set is a subspace of Pn, for an appropriate value of n

    1. All polynomials of the form p(t) = at^2, where a is in R

    2. All Polynomials of the form p(t) = a + t^2, where a is in R

    As always an explination is much more important than an answer.

    Thanks
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Ranger SVO View Post
    Its Spring Break so I've decided to get and stay caught up

    Determine if the given set is a subspace of Pn, for an appropriate value of n

    2. All Polynomials of the form p(t) = a + t^2, where a is in R
    I don't remember all the properties of a space, but 2) fails because the sum of two elements is not an element:
    (a + t^2) + (b + t^2) = (a + b) + 2t^2
    which is not an element of {a + t^2}.

    -Dan
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    Quote Originally Posted by Ranger SVO View Post

    1. All polynomials of the form p(t) = at^2, where a is in R
    Yes.

    1)k(at^2)=(ka)t^2

    2)at^2+bt^2=(a+b)t^2

    Vector subspace.
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