PROFMAT - Programa de Pós-graduação em Matemática em Rede Nacional - Sociedade Brasileira de Matematica
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Navegando PROFMAT - Programa de Pós-graduação em Matemática em Rede Nacional - Sociedade Brasileira de Matematica por Assunto "Álgebra linear"
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Item Uma proposta para o ensino de vetores no novo ensino médio usando álgebra linear: matrizes-linha e suas propriedades(Universidade Federal de Goiás, 2023-03-31) Brito, Marcos Filipe de Oliveira; Souza, Marcelo Almeida de; http://lattes.cnpq.br/1343419041226215; Souza, Marcelo Almeida de; Faria, Elisabeth Cristina de; Vieira, Vanda DomingosIn this dissertation, the proposal is presented that the teaching of vectors in High School is carried out through Mathematics, and in a consistent way, namely, we propose that a contextualized study of vectors be carried out after working with a notion of Linear Algebra using row matrices and its properties. We carried out a survey at BNCC and DC-GOEM to verify the feasibility of inserting this proposal. With vectors, many geometry problems can be solved quickly and elegantly (demonstrations of properties and theorems), and in the classroom using ICT, such as the free software GeoGebra. We present several applications of vectors using GeoGebra.Item Transformações lineares no plano e aplicações(Universidade Federal de Goiás, 2013-03-15) Nogueira, Leonardo Bernardes; Melo, Maurílio Márcio; http://lattes.cnpq.br/9171320863927413; Melo, Maurilio Márcio; Borges, Venício Veloso; Medrado, João Carlos da RochaThis paper begins with a brief history about the development of vector spaces and linear transformations, then presents fundamental concepts for the study of Linear Algebra, with greater focus on linear operators in the R2 space. Through examples it explores a wide range of operators in R2 in order to show other applications of matrices in high school and prepares the ground for the presentation a version of Spectral Theorem for selfadjoint operators in R2, which says that for every operator self-adjoint T : E!E in finite dimensional vector space with inner product, exists an orthonormal basis fu1; : : : ;ung E formed by eigenvectors of T, and culminates with their applications on the study of conic sections, quadratic forms and equations of second degree in x and y; on the study of operators associated to quadratic forms, a version of Spectral Theorem could be called as The Main Axis Theorem albeit this nomenclature is not used in this paper. Thereby summarizing a study made by Lagrange in "Recherche d’arithmétique ", between 1773 and 1775, which he studied the property of numbers that are the sum of two squares. Thus he was led to study the effects of linear transformation with integer coefficients in a quadratic form in two variables.