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Math Help - [SOLVED] Isomorphisms question

  1. #1
    joej
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    [SOLVED] Isomorphisms question

    Okay, so I want to show that the transformation
    T(a+bx+cx^2)=a+2bx+4cx^2 from P2 to P2 (from a second degree polynomial to a second degree polynomial) is an isomorphism.

    I know I have to show that ker(T)=0, but I'm not sure how to do that for this particular problem. Any ideas?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by joej View Post
    Okay, so I want to show that the transformation
    T(a+bx+cx^2)=a+2bx+4cx^2 from P2 to P2 (from a second degree polynomial to a second degree polynomial) is an isomorphism.

    I know I have to show that ker(T)=0, but I'm not sure how to do that for this particular problem. Any ideas?
    Let p(x)=a+bx+cx^2, then: T(p)(x)=a+2bx+4cx^2, and if p in ker(T), we
    have:

    T(p)(x)=a+2bx+4cx^2 = 0

    in which case we have a=0, b=0, c=0, ie p is the zero polynomial, ie ker(T)={0}.

    RonL
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