Question: Prove that T : P2(R) + P3(R) defined by T(f (x)) = xf(x) + f'(x) is a linear transformation, compute the nullity and rank of

Prove that T : P2(R) + P3(R) defined by T(f (x)) = xf(x) + f'(x) is a linear transformation, compute the nullity and rank of T, and determine whether T is one-to-one or onto

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