**Course Title:** MATLAB Programming: Applications in Engineering, Data Science, and Simulation **Section Title:** Working with Arrays and Matrices **Topic:** Create and manipulate arrays and matrices to solve a set of mathematical problems. (Lab topic) **Objective:** In this lab, you will learn to create and manipulate arrays and matrices to solve a set of mathematical problems. You will apply your knowledge of arrays and matrices to solve real-world problems, using MATLAB as a tool for calculation and visualization. **Lab Exercises:** ### Exercise 1: Creating and manipulating arrays Create an array `A` with the following elements: `[2, 5, 8, 11, 14]`. Then, perform the following operations: * Calculate the sum of all elements in the array using the `sum()` function. * Find the index of the maximum value in the array using the `find()` function. * Create a new array `B` by adding 3 to each element of `A`. ```matlab % Create array A A = [2, 5, 8, 11, 14]; % Calculate the sum of all elements in A sum_A = sum(A); % Find the index of the maximum value in A max_index = find(A == max(A)); % Create array B by adding 3 to each element of A B = A + 3; ``` ### Exercise 2: Creating and manipulating matrices Create a 2x3 matrix `C` with the following elements: ``` [1 5 9 3 7 11] ``` Then, perform the following operations: * Calculate the determinant of `C` using the `det()` function. * Find the transpose of `C` using the `transpose()` function. * Create a new matrix `D` by adding 2 to each element of `C`. ```matlab % Create matrix C C = [1 5 9; 3 7 11]; % Calculate the determinant of C det_C = det(C); % Find the transpose of C transpose_C = transpose(C); % Create matrix D by adding 2 to each element of C D = C + 2; ``` ### Exercise 3: Solving a system of linear equations Create two matrices `E` and `F` with the following elements: ``` E = [2 5; 3 7] F = [11; 14] ``` Then, solve the system of linear equations `EX = F` for `X`, where `X` is a 2x1 matrix. ```matlab % Create matrices E and F E = [2 5; 3 7]; F = [11; 14]; % Solve the system of linear equations EX = F for X X = E \ F; ``` ### Exercise 4: Visualizing arrays and matrices Create an array `G` with the following elements: `[1, 2, 3, 4, 5]`. Then, plot the elements of `G` as a line graph. ```matlab % Create array G G = [1, 2, 3, 4, 5]; % Plot the elements of G as a line graph plot(G); ``` **Key Takeaways:** * Create and manipulate arrays and matrices using MATLAB functions such as `sum()`, `find()`, `det()`, `transpose()`, and `\`. * Use MATLAB to visualize arrays and matrices as plots and charts. * Apply your knowledge of arrays and matrices to solve real-world problems, such as solving systems of linear equations. **Additional Resources:** * [MATLAB documentation on arrays and matrices](https://www.mathworks.com/help/matlab/arrays-and-matrices.html) * [MATLAB documentation on plotting and visualization](https://www.mathworks.com/help/matlab/plotting-and-data-visualization.html) **Lab Exercise Submission:** Please submit your solutions to the lab exercises as a single MATLAB script file (.m file). Make sure to include comments and headers to explain your code and identify the different exercises. **Help and Support:** If you have any questions or need help with the lab exercises, please don't hesitate to ask. Leave a comment or question below, and I will respond as soon as possible. **Next Topic:** In our next topic, we will cover conditional statements in MATLAB, including if-else and switch-case statements. You will learn how to use conditional statements to control the flow of your program and make decisions based on conditions.