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Linear Algebra and Analytical Geometry

Code 15960
Year 1
Semester S1
ECTS Credits 6
Workload TP(60H)
Scientific area Mathematics
Entry requirements Mathematics A (Secondary Education of the Science and Technology Course)
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.
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.
Main Bibliography 1) Isabel Cabral, Cecília Perdigão, Carlos Saiago, "Álgebra linear: teoria, exercícios resolvidos e
exercícios propostos com soluções", Escolar Editora, 4ª edição, 2014(MAIN BIBLIOGRAPHY).
2) Material available in Moodle & Central Library in section M-2.4
3) Álgebra linear com Aplicações, dos autores Howard Anton & Chris Rorres
4) F. R.Dias Agudo, "Introdução à Álgebra linear e geometria analítica", Escolar Editora
5) Introdução à Álgebra Linear, Reginaldo J. Santos
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
8) Evar D. Nering & John Wiley, "Linear Algebra And Matrix Theory", New York, 1970
Teaching Methodologies and Assessment Criteria The teaching-learning methodology is centred on the student, who, throughout the semester, acquires and applies the concepts, with their autonomous work. In this way, particular importance is given to the periodic assessment, which allows the student, throughout the semester, to demonstrate in stages the skills acquired through his/her work. To this end, it is planned to carry out two tests and four minitests.
Language Portuguese. Tutorial support is available in English.
Last updated on: 2024-01-18

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