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Math Help - Subspaces

  1. #1
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    Subspaces

    Suppose p1, p2, p3, p4 are specific polynomials that span a two dimensional subspace H of P5. Describe how one can find a basis for H by examining the four polynomials and making almost no computations.

    I have no idea how to do this. Someone help me please? How many elements should this basis have?
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  2. #2
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    Quote Originally Posted by Siesta View Post

    Suppose p1, p2, p3, p4 are specific polynomials that span a two dimensional subspace H of P5. Describe how one can find a basis for H by examining the four polynomials and making almost no computations.

    I have no idea how to do this. Someone help me please? How many elements should this basis have?
    two elements of a vector space are linearly independent if and only if one is not a multiple of another. now since 4 polynomials which are given to you are assumed to sapn H, they contain a basis

    for H. so all you need to do is to find two of them that are not multiple of each other. you can do that by just looking at the polynomials!
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