Question: Let T: Pn Pn be a linear transformation such that T(xk) = kxk-1 for k = 0, 1 , . . . , n.

Let T: Pn → Pn be a linear transformation such that T(xk) = kxk-1 for k = 0, 1 , . . . , n. Show that T must be the differential operator D.

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