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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- Jun 16th 2008, 01:54 PMJCIRLinear 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. - Jun 16th 2008, 02:03 PMMoo
Hello,

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 :

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

$\displaystyle T(F(x)+G(x))=T(F(x))+T(G(x))$

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..