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Matrix Representation Question

  1. Apr 22, 2012 #1
    1. The problem statement, all variables and given/known data
    This is a linear algebra matrix representation problem I have been trying to solve. I seem to keep getting it wrong, so I was hoping I could get some help.

    The linear operator T: P2-->P2 is defined by T(P(x)) = xP'(x)-P(x). B={1,x,x2}, and B'={x,1+x,-1+x2} are two ordered bases for P2.
    Find the matrix representation for T relative to the ordered basis B'. ([T]B')

    3. The attempt at a solution

    So far I have: xP'(x)-P(x) = ax2-c. Which as a matrix is: [0,-1,1;0,0,0;0,1,1] . I got this by putting ax2-c into [T(x)], [T(1+x)] and [T(-1+x2]. I have no idea if this is right or wrong, but I seem to keep making mistakes on this so any help is really appreciated.

    I know how to get [T]B which is [-1,0,0;0,0,0;0,0,1], I just keep messing up on [T]B'.
     
  2. jcsd
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