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?(adsbygoogle = window.adsbygoogle || []).push({});

So for the first one I said let u=p(x) and v=b(x)

T(u+v)=p(x)+b(x)=p(5)x^{2}+b(5)x^{2}=Tu+Tv

and T(ku)=(kp)(x)=kp(5)x^{2}=kTu

So it is a linear transformation.

For the second I said T(u+v)=p(x)+b(x)=x^{2}p(1/x)+x^{2}b(1/x)=Tp(x)+Tb(x)

and T(ku)=x^{2}kp(1/x)=k(x^{2}p(1/x))=kTp(x)

So it is also a linear transformation.

For the third I said T_{(kp)(x)}=xkp'(x)kp''(x)=k^{2}xp'(x)p''(x) which does not equal KT_{p(x)}

So it is not a linear transformation

Did I do these right?

Thanks for any help :)

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# Can Somebody Check My Proofs Please

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