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Finding the basis for a set of polynomials (linear algebra)

  1. Mar 28, 2010 #1
    Hi. Thanks for the help.
    1. The problem statement, all variables and given/known data
    Find a basis for the set of polynomials in P3 with P'(1)=0 and P''(2)=0.

    2. Relevant equations
    P' is the first derivative, P'' is the second derivative.

    3. The attempt at a solution
    The general form of a polynomial in P3 is ax^3+bx^2+cx+d
    Therefore, P' will have the form 3ax^2+2bx+c
    and P'' will have the form 6ax + 2b
    Plugging in the known values, the two equations will be:

    I just don't know where to go from there, how to find the basis. I understand the concept of a basis and how to find one for a set of matrices or vectors, but not with this. Any help would be greatly appreciated. Thank you.
  2. jcsd
  3. Mar 28, 2010 #2
    Never mind. solved.
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