Hi, would someone be able to check my proofs for me and tell me if they are right and if not what is wrong please?
So for the first one I said let u=p(x) and v=b(x)
So it is a linear transformation.
For the second I said T(u+v)=p(x)+b(x)=x^2p(1/x)+x^2b(1/x)=Tp(x)+Tb(x)
So it is also a linear transformation.
For the third I said T(kp)(x)=xkp'(x)kp''(x)=k^2xp'(x)p''(x) which does not equal KTp(x)
So it is not a linear transformation
Did I do these right?
Thanks for any help