Question

Write the MATLAB statements required to calculate and print out the squares of all the even integers between 0 and 50 . Create a table consisting of each integer and its square, with appropriate labels over each column.

Short answer

Here is the short answer to the problem: ```matlab even_integers = 0:2:50; squares = even_integers.^2; results = table(even_integers', squares', 'VariableNames', {'EvenInteger', 'Square'}); disp(results); ``` This MATLAB script initializes an array with even integers between 0 and 50, calculates their squares, and then displays the results in a table format with appropriate column labels.

Step-by-step solution

Initialize the array with even integers

To initialize an array with even integers between 0 and 50, we can use the colon operator and the following statement: ```matlab even_integers = 0:2:50; ```

Calculate the squares of each integer

Next, we will calculate the squares of each integer in the even_integers array using the element-wise square operator (`.^`). Use the following statement in MATLAB: ```matlab squares = even_integers.^2; ```

Display the results in a table format

Now that we have both the even integers and their squares, we can create a table with appropriate column labels using the table() function in MATLAB. After that, we will print the table to the Command Window using the disp() function. Here is the code to create and display the table: ```matlab results = table(even_integers', squares', 'VariableNames', {'EvenInteger', 'Square'}); disp(results); ``` Putting all the steps together, we have the following MATLAB script: ```matlab % Step 1: Initialize the array with even integers even_integers = 0:2:50; % Step 2: Calculate the squares of each integer squares = even_integers.^2; % Step 3: Display the results in a table format results = table(even_integers', squares', 'VariableNames', {'EvenInteger', 'Square'}); disp(results); ``` Run the script in MATLAB, and the output will display the squares of all even integers between 0 and 50 in a table format with column labels.

Key concepts

MATLAB arrays

In MATLAB, arrays are a fundamental concept used to store and manipulate collections of numbers systematically. In the context of the exercise provided, an array is used to store a range of even integers. The colon operator, denoted by `:` in MATLAB, is a convenient tool for creating vectors with evenly spaced elements. For instance, the statement even_integers = 0:2:50; initializes an array starting at 0, incrementing by 2, and ending at 50. This results in an array containing all even integers within that range.

Arrays in MATLAB can hold various types of data, including integers, floating-point numbers, and even characters or strings. Operations on arrays can either affect the entire array, known as array operations, or be performed element by element, referred to as element-wise operations. The array created serves as the basis for further computations and manipulations within MATLAB scripts and functions.

Element-wise operations

Element-wise operations in MATLAB are performed on corresponding elements of arrays. When we want to apply a function to each element of an array without the need for explicit loops, MATLAB's element-wise operations come in handy. The operator for element-wise exponentiation is `.^`. In the given solution, squares = even_integers.^2; raises each element of the `even_integers` array to the power of 2. The result is a new array where each element is the square of the corresponding element from the original array.

Element-wise operations are not limited to exponentiation; they include addition (`.+`), subtraction (`.-`), multiplication (`.*`), and division (`./`). By enabling operations on entire arrays rather than individual elements, MATLAB's element-wise operations greatly enhance computational efficiency and code readability. It's important to note that the arrays involved in element-wise operations must be of compatible sizes, or MATLAB will return an error.

Table formatting in MATLAB

Creating well-organized and presentable data summaries is an essential part of data analysis. MATLAB provides a 'table' data type for this purpose, which offers a convenient way to store and manipulate tabular data. In the exercise, a table is created using the table() function to display integers alongside their squares with the corresponding code: results = table(even_integers', squares', 'VariableNames', {'EvenInteger', 'Square'});.

The transposing operation (`'`) is applied to the arrays to convert them from row vectors to column vectors, which aligns with the typical table structure where each column represents a different variable. The 'VariableNames' property allows assigning descriptive names to each column, enhancing the readability of the table. Finally, the disp() function is used to print the table in the Command Window, ensuring an accessible presentation of the data. This table formatting capability in MATLAB makes it easier to understand the results and share findings in a professional manner.