Contextualization

Introduction

Matrices are a fundamental mathematical concept that has applications in various areas of study, including computer science, physics, economics, and more. A matrix is a rectangular table of numbers, symbols, or expressions, arranged in rows and columns. Matrices are classified according to the number of rows and columns and their specific characteristics. Some classifications include: identity matrix, diagonal matrix, symmetric matrix, antisymmetric matrix, among others. Each of these matrices has distinct properties and applicabilities.

The first matrix to be studied will be the Identity Matrix, a square matrix in which all elements of the main diagonal are equal to 1 and the remaining elements are equal to zero. The identity matrix is the neutral matrix in matrix multiplication operation. It is equivalent to the number 1 in real number multiplication. The second matrix to be studied is the Diagonal Matrix, which is a square matrix where all elements outside the main diagonal are equal to zero.

Contextualization

Learning about matrices is not just an academic task, but a skill that has significant practical applications. As mentioned, matrices are extremely useful in various disciplines. In computer science, for example, matrices are often used to represent graphs or networks, which in turn are used to model real-world problems such as transportation or social networks. They are also used in graphic transformations in games and design software.

In economics, matrices are used to model and solve systems of linear equations, which are common in economic problems such as determining market equilibrium. And in physics, matrices are used to represent and manipulate systems of particles, solve differential equations, among others. Thus, understanding this topic is not only relevant for those planning to pursue careers in Exact Sciences, but also for a variety of other areas where mathematics is applied.

Activity

Activity Title: "Matrices in the Real World: Classification and Applications"

Project Objective

This project aims to provide students with a deep and applied understanding of matrices and their classifications, as well as to develop technical skills in mathematics and computer science, as well as socio-emotional skills such as teamwork, time management, and problem-solving.

Project Description

In this project, student groups will be challenged to research in-depth the topic of matrices and their classifications, and apply their knowledge in a practical way by developing a Python program that is able to identify and classify matrices.

Students will be tasked with writing a code that can:

1. Recognize a matrix entered by the user.
2. Identify the type of matrix: Whether it is an identity, diagonal, symmetric, antisymmetric matrix, or none of the above.
3. Display to the user the classification of the entered matrix.

Required Materials

• Computer with internet access.
• Account on Replit, a free online programming environment that supports Python.

Step by Step

1. Group Study: Students should gather and study matrices, focusing on their different classifications. This involves understanding what each classification represents and how to identify each type of matrix.
2. Code Planning: Next, the groups should discuss and plan how to translate the acquired knowledge into an algorithm.
3. Code Development: After planning, students should divide tasks and start programming. During this phase, students will need to work together to overcome challenges and bugs that arise.
4. Testing and Adjustments: After development, groups should test their program with various matrices and make necessary adjustments.
5. Final Report: Finally, each group will need to prepare a report explaining the work done, including introduction, development, conclusions, and bibliography used.

Project Delivery

At the end of the project, each group must deliver:

1. The Code: The developed Python program, hosted on Replit. The project link must be shared with the teacher.

2. Final Report: A document must be written following the sections below:

   • Introduction: Where students will expose the theme, its relevance, application, and the project's objective.
   • Development: In this section, students must explain the theory behind matrices and their classifications, describe in detail the activity carried out, the methodology used, and present and discuss the results obtained.
   • Conclusion: Recap of the main points addressed in the project, the learnings obtained, and conclusions about the project execution.
   • Bibliography: Indication of the sources consulted for the project realization.

All documents must be delivered digitally following the teacher's guidelines.