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Math Help - Linear transformation question

  1. #1
    Junior Member
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    Linear transformation question

    I am having problem with this question

    T: P2 --->R^2 T(a+bx+cx^2)=(a,b)

    Find the basis for the kernel T and basis for the image T

    according to the text book Kernel = { T(v)= 0 }, so the kernel should look like

    T (a+bx+cx^2)=(0,0)

    how exactly do you find the basis?

    As for the image, up to my understanding, is it the entire vector space of P2 map into a subspace of R^2?
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by justin016 View Post
    I am having problem with this question

    T: P2 --->R^2 T(a+bx+cx^2)=(a,b)

    Find the basis for the kernel T and basis for the image T

    according to the text book Kernel = { T(v)= 0 }, so the kernel should look like

    T (a+bx+cx^2)=(0,0)

    how exactly do you find the basis?

    As for the image, up to my understanding, is it the entire vector space of P2 map into a subspace of R^2?
    Come on. Let (a,b)\in\mathbb{R}^2 be arbitrary.What is T(a+bx)? Also, T(a+bx+cx^2)=(a,b)=0\implies a=b=0
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