• June 16th 2008, 01:54 PM
JCIR
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.
• June 16th 2008, 02:03 PM
Moo
Hello,

Quote:

Originally Posted by JCIR
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..