12.6. Exercise Solutions

Solution to Exercise 12.1

% 12. Functions Exercises

clear % Clear all variables
clc   % Clear command window

% Exercise 12.1
fprintf("Exercise 12.1\n-------------\n")
loving_it()

% -------------------------------------------------------------------------
function loving_it()

fprintf("I'm writing MATLAB programs and I'm loving it. \n")

end

Output

Exercise 12.1
-------------

I'm writing MATLAB programs and I'm loving it. 

Solution to Exercise 12.2

Function (to be placed at the bottom of the file)

function odd_or_even(number)

if mod(number, 2) == 0
    fprintf("%d is an even number\n", number)
else
    fprintf("%d is an odd number\n", number)
end

end

Code

% Exercise 12.2
fprintf("\nExercise 12.2\n-------------\n")
odd_or_even(2)
odd_or_even(5)
odd_or_even(0)

Output

Exercise 12.2
-------------

2 is an even number
5 is an odd number
0 is an even number

Solution to Exercise 12.3

Function (to be placed at the bottom of the file)

function my_isprime(number)

prime = true;

for i = 2 : number - 1
    if mod(number, i) == 0
        fprintf("%d is not a prime number\n", number)
        return
    end
end

fprintf("%d is a prime number\n", number)

end

Code

% Exercise 12.3
fprintf("\nExercise 12.3\n-------------\n")
my_isprime(3469)
my_isprime(6137)

Output

Exercise 12.3
-------------

3469 is a prime number
6137 is not a prime number

Solution to Exercise 12.4

Function (to be placed at the bottom of the file)

function my_mean(varargin)

sum_ = 0;
for i = 1 : nargin
    sum_ = sum_ + varargin{i};
end

fprintf("mean = %0.4f\n", sum_ / nargin)
end

Code

% Exercise 12.4
fprintf("\nExercise 12.4\n-------------\n")
my_mean(1, 2, 3, 4)
my_mean(5, 3, 7, 5, 8, 2, 4, 2, 1)

Output

Exercise 12.4
-------------

mean = 2.5000
mean = 4.1111

Solution to Exercise 12.5

Function (to be placed at the bottom of the file)

% -------------------------------------------------------------------------
function norm = my_norm(vector)

norm = 0;

for i = vector
    norm = norm + i ^ 2;
end

norm = sqrt(norm);

end

Code

% Exercise 12.5
fprintf("\nExercise 12.5\n-------------")
my_norm([1, 2, 3])
my_norm([4, 5, 6, 7])

Output

Exercise 12.5
-------------

ans =

    3.7417



ans =

   11.2250

Solution to Exercise 12.6

Function (to be placed at the bottom of the file)

% -------------------------------------------------------------------------
function x = my_gcd(x, y)

while y > 0
    r = mod(x, y);
    x = y;
    y = r;
end

end

Code

% Exercise 12.6
fprintf("\nExercise 12.6\n-------------")
my_gcd(14, 245)
my_gcd(2414, 54145)

Output

Exercise 12.6
-------------

ans =

     7



ans =

    17

Solution to Exercise 12.7

Function (to be placed at the bottom of the file)

% -------------------------------------------------------------------------
function x1 = my_sqrt(x)

x0 = 0;
x1 = 1;

while abs(x1 - x0) > 5e-5
    x0 = x1;
    x1 = (x1 + x / x1) / 2;
end

end

Code

% Exercise 12.7
fprintf("\nExercise 12.7\n-------------")
my_sqrt(144)
my_sqrt(12345)

Output

Exercise 12.7
-------------

ans =

    12



ans =

  111.1081

Solution to Exercise 12.8

% Exercise 12.8
quadratic = @(x) 2 * x ^ 2 - 3 * x + 4;

fprintf("\nExercise 12.8\n-------------")
quadratic(2)
quadratic(3)

Output

Exercise 12.8
-------------

ans =

     6



ans =

    13

Solution to Exercise 12.9

Function (to be placed at the bottom of the file)

% -------------------------------------------------------------------------
function anonymous_function = power_function(k)

anonymous_function = @(x) x ^ k;

end

Code

% Exercise 12.9
square = power_function(2);
cube = power_function(3);
quartic = power_function(4);

fprintf("\nExercise 12.9\n-------------")
square(123)
cube(123)
quartic(123)

Output

Exercise 12.9
-------------

ans =

       15129



ans =

     1860867



ans =

   228886641

Solution to Exercise 12.10

Function (to be placed at the bottom of the file)

% -------------------------------------------------------------------------
function f = fibonacci(n)

if n == 1
    f = 0;

elseif n == 2
    f = 1;

else
    f = fibonacci(n - 1) + fibonacci(n - 2);
end

end

Code

% Exercise 12.10
fprintf("\nExercise 12.10\n--------------\n")
fprintf("1. The 10th Fibonacci number is %d\n", fibonacci(10))
fprintf("2. The 20th Fibonacci number is %d\n", fibonacci(20))
fprintf("3. The 40th Fibonacci number is %d\n", fibonacci(40))

Exercise 12.10
--------------

1. The 10th Fibonacci number is 34
2. The 20th Fibonacci number is 4181
3. The 40th Fibonacci number is 63245986

Solution to Exercise 12.11

Function (to be placed at the bottom of the file)

% -------------------------------------------------------------------------
function detA = my_det(A)

[m, n] = size(A);

if m ~= n
    error("Error! A must be a square array")

elseif n == 2
    detA = A(1,1) * A(2,2) - A(1,2) * A(2,1);

else
    detA = 0;
    
    for i = 1 : n
        Ai = [A(2:end,1:i-1), A(2:end,i+1:end)];
        detA = detA + (-1) ^ (i + 1) * A(1,i) * my_det(Ai);
    end
end

end

Code

% Exercise 12.11
A = [1, 2 ; 3, 4];
B = [-3, -3, 4 ; 6, -1, 3 ; -2, 6, 0];
C = [5, 2, -2, 6 ; -1, -1, 3, -1 ; 5, -1, 0, 1 ; 0, -3, 5, 2];

fprintf("\nExercise 12.11\n--------------\n")
fprintf("1. det(A) = %0.4f\n", my_det(A))
fprintf("2. det(B) = %0.4f\n", my_det(B))
fprintf("3. det(C) = %0.4f\n", my_det(C))

Output

Exercise 12.11
--------------

1. det(A) = -2.0000
2. det(B) = 208.0000
3. det(C) = 177.0000