Untitled

%% 1. Create a vector of the even whole numbers between 31 and 75.
evens = 32:2:74;

%% 2. Let x = [2, 5, 16]
x = [2, 5, 16];

% a. Add 16 to each element of x
x_a = x + 16;

% b. Add 3 to just odd index elements
x_b = x;
x_b(1:2:end) = x_b(1:2:end) + 3;

% c. Compute the square roots and squares of each element
sqrt_x = sqrt(x);
square_x = x.^2;

%% 3. Let x = [3, 2, 6, 8] and y = [4; 1; 3; 5]
x = [3, 2, 6, 8];
y = [4; 1; 3; 5];

% a. Add the sum of x to y
y_a = y + sum(x);

% b. Raise each element of x to the power of corresponding y
x_b = x.^y';

% c. Divide each element of y by corresponding element of x
y_c = y ./ x';

% d. Multiply each element of x by corresponding element of y
z = x .* y';

% e. Sum elements in 'z' and assign to 'w'
w = sum(z);

% f. Compute x*y - w
result = x * y - w;

%% 4. Create vectors
% a. 2,4,6,8,...
vec_a = 2:2:20;

% b. 10,8,6,4,2,0,-2,-4
vec_b = 10:-2:-4;

% c. 1,1/2,1/3,1/4,1/5,...
vec_c = 1 ./ (1:10);

%% 5. Create vector and sum first 100 elements
n = 1:100;
x_n = (-1).^(n+1) ./ (2*n - 1);
sum_xn = sum(x_n);

%% 6. Plot x, x^2, e^x, e^{x^2} for 0<x<4
x = linspace(0, 4, 100);
figure;
plot(x, x, 'r', x, x.^2, 'g', x, exp(x), 'b', x, exp(x.^2), 'm');
legend('x', 'x^2', 'e^x', 'e^{x^2}');
xlabel('x'); ylabel('f(x)');
title('Function Plots');

%% 7. Plot f(x) = sin(1/x) for 0.01<x<0.1
x = linspace(0.01, 0.1, 100);
y = sin(1 ./ x);
figure;
plot(x, y);
xlabel('x'); ylabel('sin(1/x)');
title('Plot of f(x) = sin(1/x)');

%% 8. Given A = [2 4 1; 6 7 2; 3 5 9]
A = [2 4 1; 6 7 2; 3 5 9];

% a. Assign first row of A to x1
x1 = A(1, :);

% b. Assign last two rows to y
y = A(2:3, :);

% c. Compute sum over columns and rows
col_sum = sum(A);
row_sum = sum(A, 2);

%% 9. Given A and B
A = [24 1; 6 7 2; 3 5 9];
B = [9 1 2 3 4 5 6 7];

% a. Assign even-numbered columns of A to B
B_even = A(:, 2:2:end);

% b. Assign odd-numbered rows to C
C = A(1:2:end, :);

% c. Convert A into a 4x3 matrix (reshaping is not possible due to dimensions)

% d. Compute reciprocal of each element of A
reciprocal_A = 1 ./ A;

% e. Compute square root of each element of A
sqrt_A = sqrt(A);

%% 10. Create a vector with integers from 21 to 35
vec_10 = 21:35;

%% 11. Create a vector of multiples of 7 from 21 to 105
vec_11 = 21:7:105;

%% 12. Create a vector with 8 equally spaced components from 6 to 9
vec_12 = linspace(6, 9, 8);

%% 13. Create a vector of square roots from 1 to 10
vec_13 = sqrt(1:10);

%% 14. Graph y = x^2 for -2 < x < 3
x = linspace(-2, 3, 100);
y = x.^2;
figure;
plot(x, y);
xlabel('x'); ylabel('y = x^2');
title('Graph of y = x^2');

%% 15. Plot y = e^(-x) and y = arctan(x) for -3 < x < 3
x = linspace(-3, 3, 100);
y1 = exp(-x);
y2 = atan(x);
figure;
plot(x, y1, 'r', x, y2, 'b');
legend('e^{-x}', 'arctan(x)');
xlabel('x'); ylabel('y');
title('Plot of e^{-x} and arctan(x)');

%% 16. Solve for Fahrenheit temperature given Celsius formula
syms F;
C = solve(5/9 * (F - 32) == -2, F);
disp(double(C));