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Math Help - Linear Algebra please help.

  1. #1
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    Linear Algebra please help.

    T: P2(R)--->P3(R) defined by T(F(x))=xf(x)+f'(x).

    I need to prove that T is a linear transformation, and say if is one 2 one or onto.
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    Hello,

    Quote Originally Posted by JCIR View Post
    T: P2(R)--->P3(R) defined by T(F(x))=xf(x)+f'(x).

    I need to prove that T is a linear transformation, and say if is one 2 one or onto.
    Note that the "object" of T is the function f, not x.

    Knowing that, you have to prove, in order to say that T is a linear transformation :

    T(aF(x))=aT(F(x)), \forall a \in \mathbb{R}^*

    T(F(x)+G(x))=T(F(x))+T(G(x))


    Or you can just say that T is the sum of linear transformations :
    - multiplying by a scalar : x
    - taking the derivative of a function, though you have to say that it's differentiable..
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