Need some help with linear transformations.

Question

anonymous · Answer

The equation I'm given is:
$$T(a _{0}+a _{1} x+a _{2} x^2)=a _{1}+2a _{2} x$$
I'm supposed to determine if it is a linear transformation from P2->P2, but I don't think it is, I think it is from a P2-> P1, I'm not sure how to prove it?

anonymous · Answer

It is differentiation, which is a linear transform.
$$T(a_0+a_1x+a_2x^2)=a_1+a_2x+0x^2$$

anonymous · Answer

I don't know what a differentiation is?  The part that confuses me is the $$2a _{2}x$$ 
They are mixed?

anonymous · Answer

oh sorry, i forgot to put in the 2.

anonymous · Answer

T(a0+a1x+a2x2)=a1+2a2x+0x2

anonymous · Answer

Right, but the A2 is with the X not the X^2

anonymous · Answer

So the right side is to the first degree so doesn't that make it a P1?

anonymous · Answer

Can anyone out there help explain this to me?

anonymous · Answer

bummer no one can explain, thanks anyway :-)