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Spanning sets and polynomial functions

  1. Mar 9, 2009 #1
    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 2? (give reasons or your answers)
    a.) 2, t^2, t, 2t^2 +3

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

    c.) 1,t^2,t^2 -2

    2. Relevant equations

    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.

    P2=a+bt+ct^2 ??
    do i need to show a,b,c can form P2 respectively ?
  2. jcsd
  3. Mar 9, 2009 #2
    If you want to show that, for instance, {2, t^2, t, 2t^2 +3} is a spanning set, then you have to find d,e,f,g (in terms of a,b,c) so that

    a+bt+ct^2 = d*(2) + e*(t^2) + f*(t) + g*(2t^2 +3)

    because every degree 2 polynomial can be written as a+bt+ct^2 and the RHS is a linear combination of the vectors in the given set.
  4. Mar 9, 2009 #3
    oh i see ,thanks for your help
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