Question

Need some help with linear transformations.

Answer 1

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?

Answer 2

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

Answer 3

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

Answer 4

oh sorry, i forgot to put in the 2.

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

Can anyone out there help explain this to me?

Answer 9

bummer no one can explain, thanks anyway :-)