Introduction

Matrices are an essential component of mathematics that have a wide range of applications in various scientific and technological fields, ranging from physics to economics. Understanding how they work and how to operate with them is a crucial step for those studying mathematics.

The operations with matrices - addition, subtraction, and multiplication - are the first steps towards a deeper understanding of the subject. Each of these operations has its own particularities and specific rules. For example, you can add and subtract matrices of the same size, but to multiply them, the number of columns in the first matrix must be equal to the number of rows in the second matrix.

Understanding these operations and knowing how to perform them correctly is essential to progress to more complex topics such as calculating determinants, matrix inversion, systems of linear equations, and even understanding vector spaces.

Contextualization

Matrices are used in a wide variety of fields, including computer science, engineering, physics, economics, and even social sciences. For example, in the field of computer science, matrices are used in image processing and game graphics. In physics, matrices are used to solve systems of linear equations that arise in the description of physical systems.

The operations with matrices are also used in engineering to analyze and design complex physical systems. For instance, in electrical engineering, matrices are used to model and analyze electrical circuits. In economics, matrices are used in a variety of ways, from analyzing inputs and outputs in an economy to optimizing decision-making processes.

Below is a list of resources where you can deepen your studies:

1. Khan Academy: Matrices (https://www.khanacademy.org/math/algebra-home/alg-matrices)
2. Matrices: operations (https://www.somatematica.com.br/emedio/matrizes/matrizes5.php)
3. Book: Linear Algebra and Its Applications - David C. Lay

Practical Activity: Matrix - Operations

Activity Title: Operations with Matrices and Real-World Applications

Activity Objective:

To understand the basic operations with matrices (addition, subtraction, and multiplication) and apply them to a real-world problem.

Activity Description:

Groups of 3-5 students will choose an application field of matrices and develop a project that solves a practical problem in the chosen field, using the operations of addition, subtraction, and multiplication with matrices.

Required Materials:

• Internet access for research.
• Paper and pen for notes.
• Calculator or computer software (such as Excel, Matlab, Python, etc.) for performing the operations.

Step by Step:

1. Choose an application field for matrices (Computer Science, Engineering, Physics, Economics, etc).
2. Research and study how the operations with matrices are used in this field.
3. Choose a real problem that can be solved through operations with matrices.
4. Perform the necessary operations to solve the problem, explaining each step in detail.
5. Report and discuss the results obtained.

Students will have one week to complete the project. The workload should be 2-4 hours per student.

Project Delivery:

After performing the operations and solving the problem, the group must meet to write a project report document containing the following topics:

1. Introduction: With contextualization of the theme, its relevance and application in the real world, and the project's objective.
2. Development: With the theory behind the operations with matrices, detailed description of the chosen problem, detailed explanation of the operations performed with the matrices, and discussion of the results obtained.
3. Conclusion: With the main points of the work, the learnings obtained, and the conclusion drawn about the application of operations with matrices in the chosen real-world problem.
4. Bibliography: With the study and research sources for the project.

By the end of the project, students should have acquired technical skills, such as performing the main operations with matrices, and socio-emotional skills, such as time management, communication, problem-solving, creative thinking, and proactivity.