9.5. Exercise Solutions#
Solution to Exercise 9.1
% 8. Arrays Exercises
clear % Clear all variables
clc % Clear command window
% Exercise 9.1
fprintf("\nExercise 9.1\n------------\n")
fprintf("1.")
a = [6, 3, 4, -1]
fprintf("2.")
B = [3, 5, -2 ; 2, 4, 3 ; 7, 2, -1]
fprintf("3.")
C = [2, 0, -1, 4 ; 7, -3, 9, -5]
fprintf("4.")
D = [-4, 4, 2 ; 7, 5, -3 ; 5, 1, 6]
fprintf("5. An array of odd numbers up to and including 31")
(1:2:31)
fprintf("6. An array containing the multiples of 6 betwee 0 and 100 inclusive")
(0:6:100)
fprintf("7. An array containing the multiples of 9 between 900 and 1000 in reverse order")
(999:-9:900)
fprintf("8. A 4x8 array of 3s")
3 * ones(4, 8)
fprintf("9. A 10x10 identity matrix")
eye(10)
Output
Exercise 9.1
------------
1.
a =
6 3 4 -1
2.
B =
3 5 -2
2 4 3
7 2 -1
3.
C =
2 0 -1 4
7 -3 9 -5
4.
D =
-4 4 2
7 5 -3
5 1 6
5. An array of odd numbers up to and including 31
ans =
Columns 1 through 14
1 3 5 7 9 11 13 15 17 19 21 23 25 27
Columns 15 through 16
29 31
6. An array containing the multiples of 6 betwee 0 and 100 inclusive
ans =
Columns 1 through 14
0 6 12 18 24 30 36 42 48 54 60 66 72 78
Columns 15 through 17
84 90 96
7. An array containing the multiples of 9 between 900 and 1000 in reverse order
ans =
999 990 981 972 963 954 945 936 927 918 909 900
8. A 4x8 array of 3s
ans =
3 3 3 3 3 3 3 3
3 3 3 3 3 3 3 3
3 3 3 3 3 3 3 3
3 3 3 3 3 3 3 3
9. A 10x10 identity matrix
ans =
1 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0
0 0 0 0 1 0 0 0 0 0
0 0 0 0 0 1 0 0 0 0
0 0 0 0 0 0 1 0 0 0
0 0 0 0 0 0 0 1 0 0
0 0 0 0 0 0 0 0 1 0
0 0 0 0 0 0 0 0 0 1
Solution to Exercise 9.2
% Exercise 9.2
fprintf("\nExercise 9.2\n------------\n")
fprintf("1. the third element of a is %d \n", a(3))
fprintf("2. the element in row 1, column 2 of B is %d \n", B(1,2))
fprintf("3. the middle two elements of a")
a(2:3)
fprintf("4. the third column of C")
C(:,3)
fprintf("5. the matrix formed by the last two rows and columns of D")
D(end-1:end,end-1:end)
fprintf("6. the matrix B with the rows in reverse order")
B(end:-1:1,:)
fprintf("7. the first and third columns of D")
D(:,1:2:3)
Output
Exercise 9.2
------------
1. the third element of a is 4
2. the element in row 1, column 2 of B is 5
3. the middle two elements of a
ans =
3 4
4. the third column of C
ans =
-1
9
5. the matrix formed by the last two rows and columns of D
ans =
5 -3
1 6
6. the matrix B with the rows in reverse order
ans =
7 2 -1
2 4 3
3 5 -2
7. the first and third columns of D
ans =
-4 2
7 -3
5 6
Solution to Exercise 9.3
% Exercise 9.3
fprintf("\nExercise 9.3\n------------\n")
fprintf("1. 2a =")
2 * a
fprintf("2. B + D =")
B + D
fprintf("3. C^T =")
C'
fprintf("4. B .* D")
B .* D
fprintf("5. DB =")
D * B
fprintf("6. DBB^T =")
D * B * B'
fprintf("7. D .^ 3 =")
D .^ 3
fprintf("8. B ^ 4 =")
B ^ 4
fprintf("9. det(B) = %0.2f \n\n", det(B))
fprintf("10. inv(B) =")
inv(B)
Output
Exercise 9.3
------------
1. 2a =
ans =
12 6 8 -2
2. B + D =
ans =
-1 9 0
9 9 0
12 3 5
3. C^T =
ans =
2 7
0 -3
-1 9
4 -5
4. B .* D
ans =
-12 20 -4
14 20 -9
35 2 -6
5. DB =
ans =
10 0 18
10 49 4
59 41 -13
6. DBB^T =
ans =
-6 74 52
267 228 164
408 243 508
7. D .^ 3 =
ans =
-64 64 8
343 125 -27
125 1 216
8. B ^ 4 =
ans =
1308 1598 133
1385 2314 510
1399 1583 452
9. det(B) = 133.00
10. inv(B) =
ans =
-0.0752 0.0075 0.1729
0.1729 0.0827 -0.0977
-0.1805 0.2180 0.0150
Solution to Exercise 9.4
% Exercise 9.4
fprintf("Exercise 9.4\n------------\n")
fprintf("1. D appended to the right of B")
[B, D]
fprintf("2. The first two rows of D appended to the bottom of B")
[B ; D(1:2,:)]
fprintf("3. D inserted between the 2nd and 3rd columns of B")
[B(:,1:2), D, B(:,3:end)]
fprintf("4. B with the middle row removed")
B(2,:) = []
fprintf("5. a sorted in descending order")
a = sort(a, 'descend')
fprintf("6. C reshaped into an 8x1 array")
C = reshape(C, 8, 1)
Output
Exercise 9.4
------------
1. D appended to the right of B
ans =
3 5 -2 -4 4 2
2 4 3 7 5 -3
7 2 -1 5 1 6
2. The first two rows of D appended to the bottom of B
ans =
3 5 -2
2 4 3
7 2 -1
-4 4 2
7 5 -3
3. D inserted between the 2nd and 3rd columns of B
ans =
3 5 -4 4 2 -2
2 4 7 5 -3 3
7 2 5 1 6 -1
4. B with the middle row removed
B =
3 5 -2
7 2 -1
5. a sorted in descending order
a =
6 4 3 -1
6. C reshaped into an 8x1 array
C =
2
7
0
-3
-1
9
4
-5