Q-1: Answer each of the following as True or False justifying your answers: a) If A = ; , then A100 , b) For any three matrices A, B and C, if AB = BA and BC = CB, then AC = CA. c) If (I – 2A")-1 = [{ ) then A = d) If A and B are 4 × 4 nonsingular matrices such that |2A¬ªB²| = 32, then 1 [0 |A| = LB2 e) Let S = {(1,0,0,0), (01,0,0), (2,3,5a,0), (a, 0,2, a – 2)} be set of vectors in R*. The set S is linearly independent if and only if a + 0. %3D

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A restaurant that is famous for its desserts offers 100 different dessertst Of these desserts, 45 contain chocolate, 30 contain nuts, and 20 contain both chocolate and nuts. You are allergic to both chocolate and nuts. How many different desserts can you order such that the dessert has neither chocolate nor nuts?

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