Practical applications of matrices and linear transformations with GeoGebra

Authors

DOI:

https://doi.org/10.14393/BEJOM-v6-2025-74190

Keywords:

Linear algebra, graph computing, GeoGebra, matrices, Linear transformations

Abstract

In this paper we present linear algebra concepts used in computer graphics. The content related to matrices and linear transformations often raises doubts in high school and college students because it is very theoretical. One way of strengthening the learning of this content is by presenting its applications. The dynamic geometry \textit{software} GeoGebra was used to demonstrate two practical applications that allow users to interact dynamically to learn concepts of linear transformations such as shear, contraction, dilation and reflections. In addition, two applications of the Fundamental Theorem of Linear Algebra were demonstrated.

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Author Biographies

  • Clésio Rodrigues da Silva Júnior, Universidade Federal de Uberlândia, Faculdade de Computação, Monte Carmelo, MG, Brasil.

    Student at the Faculty of Computing (FACOM) of the Federal University of Uberlândia.

     

  • Vania de Fátima Lemes de Miranda, Universidade Federal de Uberlândia, Instituto de Matemática e Estatística, Monte Carmelo, MG, Brasil

    Professor at the Institute of Mathematics and Statistics of the Federal University of Uberlândia, PhD in Statistics and Agricultural Experimentation. She has a master's degree in Statistics and Agricultural Experimentation, as well as a degree in Mathematics.

     

  • Giselle Moraes Resende Pereira, Universidade Federal de Uberlândia, Instituto de Matemática e Estatística, Monte Carmelo, MG, Brasil.

    Professor at the Institute of Mathematics and Statistics of the Federal University of Uberlândia, PhD in Education with an emphasis on Science and Mathematics. She has a master's degree in Mathematics, as well as a bachelor's and a teaching degree in the same area.

  • Eduardo dos Santos Rocha, Universidade Federal de Uberlândia, Faculdade de Computação, Monte Carmelo, MG, Brasil.

    Student at the Faculty of Computing (FACOM) of the Federal University of Uberlândia.

  • Luis Florial Espinoza Sánchez, Universidade Federal de Uberlândia, Instituto de Matemática e Estatística, Monte Carmelo, MG, Brasil.

    Professor at the Institute of Mathematics and Statistics of the Federal University of Uberlândia, PhD in Mathematics. He holds a master's degree and a bachelor's degree in the same area.

     

  • Danilo Elias de Oliveira, Universidade Federal de Uberlândia, Instituto de Matemática e Estatística, Monte Carmelo, MG, Brasil.

    Professor at the Institute of Mathematics and Statistics of the Federal University of Uberlândia, PhD in Applied Mathematics. He has a master's degree in Mathematics, as well as a degree in the same area.

     

References

Gonçalves, H. S. G. A importância das matrizes e transformações lineares na computação gráfica [manuscrito]. M.Sc. Thesis. Universidade Federal de Goiás, Instituto de Matemática e Estatística, 2013.

Strang, G. Álgebra Linear e Suas Aplicações. 4ª ed. São Paulo: Cengage Learning, 2010.

Lipschutz, S. and Lipson, M. Álgebra Linear. 4ª ed. Bookman, Porto Alegre, 2011.

Anton, H. and Rorres, C. Álgebra Linear com Aplicações. 8ª ed. Bookman, Porto Alegre, 2001.

Silva Junior, C. R. Tutorial Inicial Cisalhamento. 2024. Disponível em: https://github.com/clesio-junior/GeoGebra/blob/main/EtapasCisalhamentoQuadradoInicial.pdf. Acesso em: 13 out. 2024.

Gonçalves, C. S. and Sodré, U. Teorema Fundamental da Álgebra Linear. 2024. Disponível em: https://www.uel.br/projetos/matessencial/superior/alinear/teofund.htm. Acesso em: 04 dez. 2024.

GeoGebra. Aplicações de Álgebra Linear na Computação Gráfica. 2024. Disponível em: https://www.geogebra.org/f/fdx4rw7qy4. Acesso em: 19 jun. 2024.

Silva Junior, C. R. Efeito_Cisalhamento_UFU_Geogebra. 2024. Disponível em: https://www.geogebra.org/m/ay36cvxz. Acesso em: 13 mar. 2024.

Silva Junior, C. R. Tutorial da Interface de Transformações Lineares. 2024. Disponível em: https://github.com/clesio-junior/GeoGebra/blob/main/TutorialInterface.pdf. Acesso em: 14 out. 2024.

Silva Junior, C. R. Tutorial de Reprodução dos Problemas da Seção 4.3. 2024. Disponível em: https://github.com/clesio-junior/GeoGebra/blob/main/problemasSecao4.3.pdf. Acesso em: 15 out. 2024.

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Published

2025-04-30

Issue

Vol. 6 (2025): Brazilian Electronic Journal of Mathematics

Section

Applied Mathematics

License

Copyright (c) 2025 Clésio Rodrigues da Silva Júnior, Vania de Fátima Lemes de Miranda, Giselle Moraes Resende Pereira, Eduardo dos Santos Rocha, Luis Florial Espinoza Sánchez, Danilo Elias de Oliveira

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

  1. Articles published from 2025 onwards are licensed under the CC BY 4.0 license. By submitting material for publication, authors automatically agree to the journal’s editorial guidelines and affirm that the text has been properly reviewed. Simultaneous submission of articles to other journals is prohibited, as is the translation of articles published in this journal into another language without proper authorization.
  2. Articles published prior to 2025 are licensed under the CC BY-NC 4.0 license.

How to Cite

SILVA JÚNIOR, Clésio Rodrigues da; MIRANDA, Vania de Fátima Lemes de; PEREIRA, Giselle Moraes Resende; ROCHA, Eduardo dos Santos; SÁNCHEZ, Luis Florial Espinoza; OLIVEIRA, Danilo Elias de. Practical applications of matrices and linear transformations with GeoGebra. BRAZILIAN ELECTRONIC JOURNAL OF MATHEMATICS, Uberlândia, Minas Gerais, v. 6, p. 1–19, 2025. DOI: 10.14393/BEJOM-v6-2025-74190. Disponível em: https://seer.ufu.br/index.php/BEJOM/article/view/e0000. Acesso em: 8 oct. 2025.

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