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Math Help - Question regard writing linear transformation into matrix

  1. #1
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    Question regard writing linear transformation into matrix

    Hey guy, I have some problem regard to linear transformation, I can conver something like this T(x, y, z)=(x+ 2*y -z, x-y+2z,-y+z) into matrix form but I don't know how to convert "the following" into matrix form. Can you guy give me advice about how to do it?


    Let T : P3 --> P3 be the linear transformation defined by
    T(p(x)) = p(x+ 1) +p(2-x)
    (For example,  T(x^2 + 7) = (x+ 1)^2 + 7 + (2-x)^2 +7=2x^2-4x+ 18.)

    Find the matrix of T with respect to the standard basis B = {1, x, x^2, x^3} for P3.


    best regard
    Junks
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  2. #2
    MHF Contributor
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    Re: Question regard writing linear transformation into matrix

    Start by writing out explicitly the value of T on an arbitrary cubic polynomial ax + bx + cx + d.
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