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Question 6. onsider the function L Pa R3 given by L (p)) (a) (p(0), p (0), p (0). Answer yes/no to the following questions and justify your answer. (i) Is L injective? Solution Choose p1 3, p2 J 2a3 03, 3.02, 6.0 L(pi) (ar) (0,0,0) L(pa)l(ar) (2.03, 6.02, 12 0) 0, 0, 0) Note that L (pi))(a) L(p2))(a) but 1 2 Thus L is not injective. (ii) Is L surjective? Solution lety E R3. Thus we have p (a 0 (iii) Is L linear (iv) Does L have an inverse? If yes, what is it? If no, why not?

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