Question

# Consider the below matrixA, which you can copy and paste directly into Matlab.

Problem #1: Consider the below matrix A, which you can copy and paste directly into Matlab. The matrix contains 3 columns. The first column consists of Test #1 marks, the second column is Test # 2 marks, and the third column is final exam marks for a large linear algebra course. Each row represents a particular student.

A = [36 45 75 81 59 73 77 73 73 65 72 78 65 55 83 73 57 78 84 31 60 83 93 66 75 74 91 85 64 55 83 94 65 81 92 71 56 58 75 93 87 74 83 83 72 84 56 76 59 72 46 52 79 54 60 75 72 73 63 78 74 78 56 80 84 85 70 86 62 58 75 85 49 92 79 64 66 90 73 69 81 81 76 67 70 72 100 77 85 59 44 60 80 66 57 59 76 42 80 59 66 73 95 80 64 92 80 81 84 73 88 56 68 59 84 71 66 77 97 81 53 100 64 83 72 84 99 51 87 75 48 57 76 89 78 90 64 50 69 35 55 100 71 68 75 72 71 83 82 72 64 75 64 85 96 58 93 84 92 69 82 84 71 90 66 66 92 67 65 59 58 68 83 66 67 82 88 76 68 73 62 71 74 74 82 87 57 86 86 58 55 57 79 89 78 90 92 62 69 99 77 89 52 85 60 77 99 69 54 70 84 86 86 70 65 100 47 92 84 93 74 81 86 70 72 83 82 71 55 87 92 100 65 92 90 69 69 100 65 77 100 67 100 89 62 72 93 99 77 36 68 99 77 31 89 78 79 87 72 89 73 89 96 59 100 84 100 73 89 98 81 53 55 61 80 72 56 66 80 59 78 69 70 57 63 83 88 98 69 86 72 65 58 51 59 73 69 73 96 100 97 63 83 90 85 90 90 52 100 86 79 73 76 83 42 67 64 74 80 75 78 81 53 66 69 100 79 71 85 77 100 72 80 84 100 53 75 66 52 88 38 78 60 86 67 93 78 73 66 78 96 35 79 84 64 96 99 84 77 65 65 63 63 91 97 60 65 84 90 69 79 79 60 100 60 57 74 80 64 77 46 72 78 88 48 43 73 71 75 52 100 68 73 65 52 100 66 88 65 73 91 65 82 90 42 78 50 74 80 79 100 85 81 70 73 50 95 100 98 83 76 94 59 82 68 82 82 67 74 68 64 81 79 84 96 73 71 69 81 90 88 92 85 89 86 87 75 58 66 90 86 58 70 85 81 84 44 98 88 59 71 91 56 79 85 59 74 67 100 76 83 71 87 82 83 77 64 40 64 55 100 62 57 80 69 70 77 56 46 71 72 70 63 97 72 53 83 96 84 91 91 86 73 87 91 63 61 72 49 46 61 71 84 82 83 60 61 41 91 98 77 64 72 69 57 71 80 74 57 85;59 63 90 100 77 52 96 56 75 41 78 66 99 50 70 90 75 83 79 65 57 79 100 72 90 67 70 51 70 74 100 100 63 73 85 83 61 47 84 99 49 69 58 73 68 100 88 62 75 98 57 64 84 89 86 97 73 63 68 100 59 49 79 45 59 77 94 81 60 50 66 75 80 70 73 89 50 49 71 47 57 98 55 63 51 64 66 79 76 55 47 82 45 88 66 77 77 77 72 60 67 86 85 69 88 65 95 67 72 81 76 49 50 68 65 78 83 48 79 81 81 89 96 55 98 63 90 74 92 65 75 57 67 62 66 72 65 59 79 62 84 68 79 70 76 46 30 51 63 53 99 37 66 72 83 64 74 87 89 57 74 88 63 68 59 68 90 60 80 28 80 61 64 47 62 82 58 60 61 83 66 90 62 69 64 69 68 56 78 48 88 76 64 45 67 64 86 68 88 100 73 74 79 71 50 90 83 77 81 67 76 50 100 100 96 74 100 70 60 70 66 73 56 86 75 83 72 68 67 69 92 77 67 44 84 72 59 74 58 76 51 100 68 55 94 86 73 49 72 73 68 73 83 42 59 55 59 75 76 73 67 55 65 81 52 57 69 58 69 54 69 71 65 61 76 83 77 80 55 81 57 54 71 61 80 62 77 86 78 77 78 61 60 72 54 72 62 57 80 53 84 58 57 55 89 48 78 73 68 86 100 79 75 59 90 77 81 47 58 82 90 69 58 63 84 50 84 84 92 79 64 68 25 70 79 68 73 72 58 61 54 76 57 76 77 83 51 58 52 72 76 72 63 51 79 75 69 48 59 67 84 65 71 90 83 80 66 81 69 77 87 90 87 73 97 77 65 60 85 84 65 72 55 86 79 80 33 54 51 70 77 65 90 59 49 58 78 73 76 94 68 74 90 45 63 93 71 92 66 35 62 67 81 91 68 79 55 75 62 68 49 76 100 73 46 79 93 95 57 49 91 94 86 70 76 61 74 76 76 100 31 86 81 65 60 68 85 58 80 58 76 93 81 71 55 76 90 46 92 57 74 73 79 72 55 74 60 73 75 66 100 78 75 71 77 93 87 64 93 45 84 50 52 72 75 42 84 70 86 68 82 66 61 79 71 63 86 55 59 41 100 81 83 89 69 63 66 71 63 69 66 71 79 63 59 63 87 78 80 64 81 58 58 59 82 70 74 65 92 54;53 62 42 62 77 73 45 53 63 71 73 79 78 79 61 54 51 62 48 58 69 81 53 67 88 43 68 68 61 42 51 91 47 66 66 55 43 87 100 69 51 43 52 70 58 45 100 75 89 36 52 79 53 61 61 61 45 52 88 41 33 64 68 80 87 83 11 48 76 74 56 70 76 78 65 40 62 60 70 78 80 45 94 72 70 64 67 62 54 48 54 74 84 82 49 43 85 60 54 65 58 49 51 58 62 45 59 56 34 85 65 53 79 74 63 76 59 32 71 58 64 77 65 40 74 75 63 48 47 63 77 58 58 83 69 65 67 58 60 50 39 52 71 72 79 43 49 58 57 60 49 68 85 73 61 65 65 88 69 64 69 50 47 66 54 68 74 67 47 86 59 37 35 85 50 57 45 48 85 41 69 70 92 82 32 46 76 16 70 70 58 74 95 52 56 54 75 52 69 54 35 47 43 50 75 47 58 60 46 65 74 45 75 68 89 75 71 100 51 59 57 60 61 63 39 57 51 66 49 38 43 52 56 100 58 51 72 43 64 65 81 72 84 56 57 59 57 27 52 58 52 71 67 56 69 94 85 42 86 64 100 52 29 46 33 59 52 69 73 71 92 50 90 60 49 43 33 72 60 77 53 59 50 59 39 71 58 56 84 62 70 54 48 54 77 74 45 72 55 96 89 40 78 79 67 65 68 59 55 46 52 54 54 42 66 83 43 75 68 46 92 65 60 81 52 64 71 65 57 83 77 53 54 67 58 48 65 54 68 74 54 66 66 74 86 72 24 70 64 60 64 37 58 43 72 79 49 86 47 100 70 40 67 54 76 58 86 88 35 71 60 68 79 68 55 60 98 37 67 56 62 57 82 56 66 72 61 71 69 70 58 66 50 43 63 77 80 47 58 37 50 60 49 39 68 57 67 87 74 52 70 81 79 52 36 92 69 72 58 100 62 73 65 57 62 68 51 23 54 51 49 71 64 57 62 83 62 68 64 76 59 22 52 42 62 71 62 78 27 48 34 70 72 68 49 93 95 52 52 77 91 74 50 89 58 49 53 64 50 55 50 72 53 56 53 49 68 82 44 59 62 51 37 63 55 63 58 54 54 80 88 49 54 32 53 54 61 61 43 72 87 69 73 62 55 60 65 96 61 35 76 64 73 70 67 55 75 72 58 43 58 71 58 54 73 69 41 67 73 58]'

Before doing the below parts, you can check that you are on the right track as follows. Use a boolean expression, followed by the sum function, to verify that 296 students got a higher mark on Test #1 than on Test # 2.

(a) How many students got a higher mark on the exam than on Test #1?

(b) How many students had marks that increased throughout the term? ie, how many students had test scores such that Test #1 < Test #2 < Exam? (Or equivalently, Test #1 < Test #2 and Test #2 < Exam)

(c) How many students got a mark of 90 or higher on at least one of the tests or exam? (i.e, got a mark of 90 or higher on Test  #1 or Test #2 or the Exam)

Part a

ans =

152

Part b

ans =

39

Part c

ans =

150

MATLAB CODE

clear, clc
A = [36 45 75 81 59 73 77 73 73 65 72 78 65 55 83 73 57 78 84 31 60 83 93 66 75 74 91 85 64 55 83 94 65 81 92 71 56 58 75 93 87 74 83 83 72 84 56 76 59 72 46 52 79 54 60 75 72 73 63 78 74 78 56 80 84 85 70 86 62 58 75 85 49 92 79 64 66 90 73 69 81 81 76 67 70 72 100 77 85 59 44 60 80 66 57 59 76 42 80 59 66 73 95 80 64 92 80 81 84 73 88 56 68 59 84 71 66 77 97 81 53 100 64 83 72 84 99 51 87 75 48 57 76 89 78 90 64 50 69 35 55 100 71 68 75 72 71 83 82 72 64 75 64 85 96 58 93 84 92 69 82 84 71 90 66 66 92 67 65 59 58 68 83 66 67 82 88 76 68 73 62 71 74 74 82 87 57 86 86 58 55 57 79 89 78 90 92 62 69 99 77 89 52 85 60 77 99 69 54 70 84 86 86 70 65 100 47 92 84 93 74 81 86 70 72 83 82 71 55 87 92 100 65 92 90 69 69 100 65 77 100 67 100 89 62 72 93 99 77 36 68 99 77 31 89 78 79 87 72 89 73 89 96 59 100 84 100 73 89 98 81 53 55 61 80 72 56 66 80 59 78 69 70 57 63 83 88 98 69 86 72 65 58 51 59 73 69 73 96 100 97 63 83 90 85 90 90 52 100 86 79 73 76 83 42 67 64 74 80 75 78 81 53 66 69 100 79 71 85 77 100 72 80 84 100 53 75 66 52 88 38 78 60 86 67 93 78 73 66 78 96 35 79 84 64 96 99 84 77 65 65 63 63 91 97 60 65 84 90 69 79 79 60 100 60 57 74 80 64 77 46 72 78 88 48 43 73 71 75 52 100 68 73 65 52 100 66 88 65 73 91 65 82 90 42 78 50 74 80 79 100 85 81 70 73 50 95 100 98 83 76 94 59 82 68 82 82 67 74 68 64 81 79 84 96 73 71 69 81 90 88 92 85 89 86 87 75 58 66 90 86 58 70 85 81 84 44 98 88 59 71 91 56 79 85 59 74 67 100 76 83 71 87 82 83 77 64 40 64 55 100 62 57 80 69 70 77 56 46 71 72 70 63 97 72 53 83 96 84 91 91 86 73 87 91 63 61 72 49 46 61 71 84 82 83 60 61 41 91 98 77 64 72 69 57 71 80 74 57 85;59 63 90 100 77 52 96 56 75 41 78 66 99 50 70 90 75 83 79 65 57 79 100 72 90 67 70 51 70 74 100 100 63 73 85 83 61 47 84 99 49 69 58 73 68 100 88 62 75 98 57 64 84 89 86 97 73 63 68 100 59 49 79 45 59 77 94 81 60 50 66 75 80 70 73 89 50 49 71 47 57 98 55 63 51 64 66 79 76 55 47 82 45 88 66 77 77 77 72 60 67 86 85 69 88 65 95 67 72 81 76 49 50 68 65 78 83 48 79 81 81 89 96 55 98 63 90 74 92 65 75 57 67 62 66 72 65 59 79 62 84 68 79 70 76 46 30 51 63 53 99 37 66 72 83 64 74 87 89 57 74 88 63 68 59 68 90 60 80 28 80 61 64 47 62 82 58 60 61 83 66 90 62 69 64 69 68 56 78 48 88 76 64 45 67 64 86 68 88 100 73 74 79 71 50 90 83 77 81 67 76 50 100 100 96 74 100 70 60 70 66 73 56 86 75 83 72 68 67 69 92 77 67 44 84 72 59 74 58 76 51 100 68 55 94 86 73 49 72 73 68 73 83 42 59 55 59 75 76 73 67 55 65 81 52 57 69 58 69 54 69 71 65 61 76 83 77 80 55 81 57 54 71 61 80 62 77 86 78 77 78 61 60 72 54 72 62 57 80 53 84 58 57 55 89 48 78 73 68 86 100 79 75 59 90 77 81 47 58 82 90 69 58 63 84 50 84 84 92 79 64 68 25 70 79 68 73 72 58 61 54 76 57 76 77 83 51 58 52 72 76 72 63 51 79 75 69 48 59 67 84 65 71 90 83 80 66 81 69 77 87 90 87 73 97 77 65 60 85 84 65 72 55 86 79 80 33 54 51 70 77 65 90 59 49 58 78 73 76 94 68 74 90 45 63 93 71 92 66 35 62 67 81 91 68 79 55 75 62 68 49 76 100 73 46 79 93 95 57 49 91 94 86 70 76 61 74 76 76 100 31 86 81 65 60 68 85 58 80 58 76 93 81 71 55 76 90 46 92 57 74 73 79 72 55 74 60 73 75 66 100 78 75 71 77 93 87 64 93 45 84 50 52 72 75 42 84 70 86 68 82 66 61 79 71 63 86 55 59 41 100 81 83 89 69 63 66 71 63 69 66 71 79 63 59 63 87 78 80 64 81 58 58 59 82 70 74 65 92 54;53 62 42 62 77 73 45 53 63 71 73 79 78 79 61 54 51 62 48 58 69 81 53 67 88 43 68 68 61 42 51 91 47 66 66 55 43 87 100 69 51 43 52 70 58 45 100 75 89 36 52 79 53 61 61 61 45 52 88 41 33 64 68 80 87 83 11 48 76 74 56 70 76 78 65 40 62 60 70 78 80 45 94 72 70 64 67 62 54 48 54 74 84 82 49 43 85 60 54 65 58 49 51 58 62 45 59 56 34 85 65 53 79 74 63 76 59 32 71 58 64 77 65 40 74 75 63 48 47 63 77 58 58 83 69 65 67 58 60 50 39 52 71 72 79 43 49 58 57 60 49 68 85 73 61 65 65 88 69 64 69 50 47 66 54 68 74 67 47 86 59 37 35 85 50 57 45 48 85 41 69 70 92 82 32 46 76 16 70 70 58 74 95 52 56 54 75 52 69 54 35 47 43 50 75 47 58 60 46 65 74 45 75 68 89 75 71 100 51 59 57 60 61 63 39 57 51 66 49 38 43 52 56 100 58 51 72 43 64 65 81 72 84 56 57 59 57 27 52 58 52 71 67 56 69 94 85 42 86 64 100 52 29 46 33 59 52 69 73 71 92 50 90 60 49 43 33 72 60 77 53 59 50 59 39 71 58 56 84 62 70 54 48 54 77 74 45 72 55 96 89 40 78 79 67 65 68 59 55 46 52 54 54 42 66 83 43 75 68 46 92 65 60 81 52 64 71 65 57 83 77 53 54 67 58 48 65 54 68 74 54 66 66 74 86 72 24 70 64 60 64 37 58 43 72 79 49 86 47 100 70 40 67 54 76 58 86 88 35 71 60 68 79 68 55 60 98 37 67 56 62 57 82 56 66 72 61 71 69 70 58 66 50 43 63 77 80 47 58 37 50 60 49 39 68 57 67 87 74 52 70 81 79 52 36 92 69 72 58 100 62 73 65 57 62 68 51 23 54 51 49 71 64 57 62 83 62 68 64 76 59 22 52 42 62 71 62 78 27 48 34 70 72 68 49 93 95 52 52 77 91 74 50 89 58 49 53 64 50 55 50 72 53 56 53 49 68 82 44 59 62 51 37 63 55 63 58 54 54 80 88 49 54 32 53 54 61 61 43 72 87 69 73 62 55 60 65 96 61 35 76 64 73 70 67 55 75 72 58 43 58 71 58 54 73 69 41 67 73 58]';
disp('Part a');
numel(find(A(:,3)>A(:,1)))
disp('Part b');
numel(find(A(:,1) disp('Part c');
numel(find(A(:,1)>=90|A(:,2)>=90|A(:,3)>=90))

Kindly revert for any queries

Thanks.

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