Question: Problem 4. (a) Let V be a finite-dimensional vector space and let T : V - V be a linear transformation. Show that T is

Problem 4. (a) Let V be a finite-dimensional vector space and let T : V - V be a linear transformation. Show that T is surjective if and only if T is injective. [HINT: Rank-Nullity.] (b) Show that the mapping f : R2 - R2 defined by f ( ) evis injective but not surjective. Explain why this does not contradict the result from (a). (c) Show that the mapping D : P - P defined by D(f) = f' is surjective but not injective. Explain why this does not contradict the result from (a)

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