16. (2 marks) Given the following Matrix A = i find the inverse by using Gauss Jordan algorithm [A|I]. Which elementary operation give you A- . a) Ri - R1 - 3R2 . c) R2 - R1 - 3R2 . b) R1 - R1 + 3R2 . d) R1 + R2 - 3R1 17. ( 2 marks) 3 0 0 A = 0 2 O 1/3 0 0 1/3 0 0 . a) Al = 0 1/2 0 . C) Al 0 1/2 0 0 0 -1/5 O 0 1/5 3 0 0 . b) A-1 = 10 0 1/3 0 1/2 0 0 . d) A-1 = -1/2 0 O -1/5 Oo 0 -1/5 18. ( 2 marks) A = . a) det A=-8 . c) det A=3 . b) det A=-11 . d) det A=11 Question 1 continues on the next page. . . Final Exam Fall: 2022 MATH 163 Page 7 of 14 19. ( 3 marks) Find Maximum of C(x, y) = 2x - 3y over the following closed convex region 60 55 50 45 40 35 30 25 20 15 10 5 0 5 10 15 20 25 30 35 40 45 50 55 60 a) 100 . C) 95 . b) -165 . d) 0 20. (1 mark) A, B events such that Pr(A) = 0.4 and Pr(An B) = 0.2. Find Pr(B | A) . a) 0.3 . c) 0.5