Question: Let T: P2 P2 be the linear transformation defined by T(p(x)) = xp'(x). (a) Which, if any, of the following polynomials are in ker(

Let T: P2 → P2 be the linear transformation defined by T(p(x)) = xp'(x).
(a) Which, if any, of the following polynomials are in ker( T)?
(i) 1
(ii) x
(iii) x2
(b) Which, if any, of the polynomials in part (a) are in range(T)?
(c) Describe ker(T) and range(T).

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