Linear transformation D:P2 --> P2

[gildee]

Linear transformation D:Psub2 to Psub2 defined by
D( Asub0 + Asub1x + Asub2x^2) = Asub1 + 2Asub2x

Find the matrix of this linear transformation with respect to the
ordered bases C to C, where C= { 1-x , 1+ x, x^2 }


I know that D stands for differentiating .
D prime is Asub1 + 2Asub2x

I think the matrix is

1 1 2
-1 1 0

I would like to know if my matrix is correct?

Thanks

 

[WWGD]

But differentiation maps into $P_1$ . You may embed $P_1$ in $P_2$, but the map is into $P_1$ otherwise.

 

[phyzguy]

Your answer cannot be complete. For one thing, it should be a 3x3 matrix.

 

[WWGD]

And then you just need to make sure that the matrix T representing D takes the basis to where it should, i.e., to D(basis)=D(1+x + 1-x +x^2).