| Code |
8620
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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 0 - Motivation for Linear Algebra
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: properties, diagonalizable matrices.
Chapter 7 ( Analytical Geometry) - Vector calculus: inner product and vectorial product.
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Main Bibliography |
1) Isabel Cabral, Cecília Perdigão, Carlos Saiago, "Álgebra linear: teoria, exercícios resolvidos e
exercícios propostos com soluções", Escolar Editora, 4ª edição, 2014.
2) Material available in Moodle & Central Library in section M-2.4
3) Álgebra linear com Aplicações, dos autores Howard Anton & Chris Rorres
https://www.professores.uff.br/jcolombo/wpcontent/
uploads/sites/124/2018/08/Algebra_Linear_com_Aplica_10_-Edi_Anton_Rorres.pdf
4) F. R.Dias Agudo, "Introdução à Álgebra linear e geometria analítica", Escolar Editora
5) Introdução à Álgebra Linear, Reginaldo J. Santos
(http://gradmat.ufab.edu.br/disciplinas/listas/alglin/gaalt00.pdf)
6) Luís T. Magalhães, "Álgebra linear como introdução à matemática aplicada", Escolar Editora, 2001.
7) Seymour Lipschutz, "Álgebra linear: resumo da teoria, 600 problemas resolvidos, 524 problemas
propostos"
8) Evar D. Nering & John Wiley, "Linear Algebra And Matrix Theory", New York, 1970
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Language |
Portuguese. Tutorial support is available in English.
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