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Spanning sets of polynomial functions

  1. Mar 10, 2008 #1
    [SOLVED] Spanning sets of polynomial functions (urgent)

    1. The problem statement, all variables and given/known data
    Which o the following are spanning sets for the vector space P2 of polynomial functions of degree [tex]\leq[/tex]2? (give reasons or your answers)

    a.) 2, t^2, t, 2t^2 +3

    b.)t+2, t^2 -1

    3. The attempt at a solution

    I'm not entirely sure how to do this but i think i need to show that any vector in P2 can be written as a linear combination of the elements in the set.

    So for a.) i wrote out the generic polynomial of P2 with scalar coefficients:

    at^2 + bt + c= 2p + qt^2 + xt + 2yt^2 + 3z

    In this case a = q+2y, b = x, c = 2p+3z

    I then put this into an augmented matirx and reduced it to:

    p 0 0 0 3z/a c/a
    0 q 0 2y 0 a
    0 0 x 0 0 b

    I don't really know what i am supposed to do from here, i was just following a worked example but the conclusion is unclear in it and i don't knoaw what to do. I followed the same procedure or b.) and got this augmented matrix:

    a -b/2 0 z/2
    0 0 0 x-z
    0 0 0 y+z

    Im a bit unsure if this is right, but i don't know how to proceed. Any help please, urgent also.
    Last edited: Mar 10, 2008
  2. jcsd
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