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Homework Help: Linear transformation D:P2 --> P2

  1. Mar 9, 2015 #1
    • Moved from a technical forum section, so missing the template
    Linear transformation D:Psub2 to Psub2 defined by
    D( Asub0 + Asub1x + Asub2x^2) = Asub1 + 2Asub2x

    Find the matrix of this linear transformation with respect to the
    ordered bases C to C, where C= { 1-x , 1+ x, x^2 }

    I know that D stands for differentiating .
    D prime is Asub1 + 2Asub2x

    I think the matrix is

    1 1 2
    -1 1 0

    I would like to know if my matrix is correct?

  2. jcsd
  3. Mar 9, 2015 #2


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    But differentiation maps into ## P_1 ## . You may embed ##P_1## in ## P_2##, but the map is into ##P_1## otherwise.
  4. Mar 9, 2015 #3


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    Your answer cannot be complete. For one thing, it should be a 3x3 matrix.
  5. Mar 9, 2015 #4


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    And then you just need to make sure that the matrix T representing D takes the basis to where it should, i.e., to D(basis)=D(1+x + 1-x +x^2).
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