Contextualization

Mathematics is the science that helps us understand the world we live in, and many of its applications are present in our daily lives, even if subtly and imperceptibly. The study of Determinants is one of these cases, forming the basis for understanding complex mathematical systems, being a fundamental tool in the study of linear algebra and finding practical applications in various areas such as physics, economics, engineering, computer graphics, among others.

For today's project, we will focus on something simpler - 1x1 Determinants. These are the most basic cases of determinants and are the beginning of understanding how this mathematics works. The simplicity of the 1x1 determinant allows us to explore and understand the basic concepts behind this powerful tool.

Introduction

Determinants are mathematical functions associated with square matrices. The determinant of a 1x1 matrix, that is, a matrix that contains only one number, is simply that number. For example, the determinant of the matrix [4] is 4.

Although it seems strangely simple, the ability to calculate determinants is crucial for understanding larger and more complex matrices. Determinants are used to solve systems of equations, find the inverse of a matrix, and are fundamental in the theory of calculus of several variables.

Reiterating, the study of determinants begins with the understanding of a 1x1 determinant, a matrix consisting of a single number. Consequently, this will be the basis for us to learn about larger matrices.

Practical Activity

Activity Title: "Determinants 1x1 in the Real World"

Project Objective:

The objective of this project is to allow students to explore the concept of 1x1 determinants by solving practical and real-life problems. Through this activity, students will solidify the theory in a playful and engaging way, using mathematics as a tool to solve practical problems.

Detailed Project Description:

Divided into groups of 3 to 5 students, each group will be tasked with identifying a real-world situation where the concept of determinants can be applied. It will be necessary to create and solve a mathematical problem related to this situation. The students must then document the resolution process in a detailed report.

The activity will be divided into 3 main parts: Research and problem elaboration, problem solving, and report writing.

1. Research and Problem Elaboration: Groups must research and choose a real-world situation where the concept of determinants can be used. From this situation, students must create a mathematical problem that uses the 1x1 determinant in its resolution.

2. Problem Solving: With the problem formulated, students must solve it using the concept of determinants. It is important to show all the steps of the resolution, so that the reasoning behind the solution can be understood.

3. Report Writing: Finally, the groups must write a detailed report explaining the chosen situation, the formulated problem, the problem's resolution, and the importance of determinants for solving the problem.

Required Materials:

• Computer with internet access to research possible applications of the 1x1 determinant.
• Paper and pen for sketching ideas and calculations.
• Word processing program for report writing.

Detailed Step-by-Step for Activity Execution:

1. The group should start by holding a meeting to discuss possible real-world scenarios where determinants can be applied and choose one of them.

2. With the chosen scenario, the group should create a mathematical problem that can be solved using the concept of the 1x1 determinant.

3. The created problem should be solved step by step, with all calculations and reasoning described to facilitate understanding for those reading the report.

4. Finally, the group should write the report, which should include the following items: Introduction to the topic, description of the problem, detailed problem resolution, conclusions, and bibliography used.

The conclusion of the report should relate the theory learned to the practice carried out, highlighting the importance and applicability of determinants in the real world.

The report must be submitted one week after the start of the project.

Report:

The report is a crucial part of the project and must follow a specific structure:

1. Introduction: Students must present the project theme and explain its relevance, contextualizing its real-world application.

2. Development: Here, the problem that was created and solved should be detailed, explaining all the steps of the resolution. In addition, the theory that underlies the solution, that is, the concept of 1x1 determinants, should be addressed.

3. Conclusion: Students must conclude the report by revisiting its main points, such as the importance of 1x1 determinants and their practical application. They should also report what they learned from the project.

4. Bibliography: Here, students must list all the sources they used to elaborate the work, such as books, internet pages, and videos.