| Code |
15960
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| Year |
1
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| Semester |
S1
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| ECTS Credits |
6
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| Workload |
TP(60H)
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| Scientific area |
Mathematics
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Entry requirements |
Mathematics A (Secondary Education of the Science and Technology Course)
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Learning outcomes |
At the end of the curricular unit, the student should be able to:
- Compute the sum, the product, and the transpose of a matrix;
- Compute the rank of a matrix;
- Identify an invertible matrix and compute its inverse;
- Solve and classify systems of linear equations;
- Identify subspaces of a vector space and compute a base;
- Compute the matrix of a linear transformation;
- Solve systems of linear equations and compute the inverse of a matrix using determinants;
- Compute the eigenvalues of a matrix;
- Identify the most important properties of an inner product and vectorial product.
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Syllabus |
Chapter 1 - Matrices: definition of real and complex matrices, operations with matrices; elementary operations for condensation, rank of a matrix, inverse of a matrix
Chapter 2 - Systems of Linear Equations: definition and extended matrix associated with the system, resolution and classification of a system.
Chapter 3 - Determinants: determinant of a square matrix, Laplace's theorem, properties, the Adjoint and the inverse of a matrix, application to systems of linear equations.
Chapter 4 - Vector Spaces: definition of vector space, subspaces, linear combinations, generator set, linear independence, base and dimension, base change matrix.
Chapter 5 - Linear Transformations: definition and examples, properties, image and core of subspace, matrix of a linear transformation.
Chapter 6 - Eigenvalues and eigenvectors: definitions, diagonalizable matrix.
Chapter 7 ( Analytical Geometry) - Vector calculus: inner product and vectorial product.
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Main Bibliography |
1) Rogério Serôdio, Álgebra Linear, livro escrito pelo docente e disponibilizado no Moodle.
2) Isabel Cabral, Cecília Perdigão, Carlos Saiago, "Álgebra linear: teoria, exercícios resolvidos e
exercícios propostos com soluções", Escolar Editora, 4ª edição, 2014 (BIBLIOGRAFIA PRINCIPAL).
3) Material disponibilizado no Moodle & Biblioteca central na secção M-2.4
4) Álgebra linear com Aplicações, dos autores Howard Anton & Chris Rorres
5) F. R.Dias Agudo, "Introdução à Álgebra linear e geometria analítica", Escolar Editora
6) Introdução à Álgebra Linear, Reginaldo J. Santos
7) Luís T. Magalhães, "Álgebra linear como introdução à matemática aplicada", Escolar Editora, 2001.
8) Seymour Lipschutz, "Álgebra linear: resumo da teoria, 600 problemas resolvidos, 524 problemas
propostos"
9) Evar D. Nering & John Wiley, "Linear Algebra And Matrix Theory", New York, 1970
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Teaching Methodologies and Assessment Criteria |
Teaching–learning methodology: student-centred approach with short expository moments, problem solving, and guided independent work. Assessment is continuous: two mid-semester tests and regular activities (e.g., Kahoot and interactive exercises) that contribute to the final grade, encouraging steady study and frequent feedback. A competency-based model is implemented: 51 competencies across six chapters are validated orally throughout the semester. Each student may choose which competencies to validate and when, and may repeat attempts until mastery is demonstrated. Validations are brief, focused on understanding and application, with immediate feedback and an individual progress record.
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Language |
Portuguese. Tutorial support is available in English.
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