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- Linear Algebra

Code | 8535 |

Year | 1 |

Semester | S1 |

ECTS Credits | 6 |

Workload | TP(60H) |

Scientific area | Mathematics |

Entry requirements | Mathematics A of High School (10.º, 11.º, 12.º) |

Mode of delivery | Face-to-Face |

Work placements | Not applicable |

Learning outcomes | The curricular unit is an introduction to Linear Algebra. It is intended to develop mathematical, logical, critical and analytical reasoning and student’s autonomy when formulating and solving problems. Concretely, at the end of the curricular unit, the student should be able to: make operations over/with matrices and apply properties; determine the rank of a matrix; classify and solve, using matrices, systems of linear equations; apply properties of the inverse of a regular matrix and determine it; calculate the determinant of a square matrix and apply properties; solve problems of Analytic Geometry; identify/sketch quadric surfaces; decide the linear independence/dependence of vectors; characterize a spanned subspace; determine the dimension of a linear space; represent a linear application by a matrix; calculate eigenvalues and eigenvectors, and apply properties; interpret and use mathematical language. |

Syllabus |
1: Matrices and Systems of Linear Equations Real and complex matrices. Matrix operations. Elementary operations. Resolution of systems of linear equations. Inverse of a matrix. 2: Determinants Determinant of a square matrix, properties; Laplace's theorem. The Adjoint and the inverse of a matrix; Application to systems of linear equations; 3: Vector Spaces Definition of vector space. Subspaces. Linear Combinations. Linear independence and dimension. 4: Linear Transformations Definition and examples. Properties. Matrices and linear transformations. 5: Eigenvalues and eigenvectors of a matrix. 6: Analytical Geometry Vector calculus: inner product and vectorial product; The plane, the line; |

Main Bibliography |
-- Cabral, I., Perdigão, C., Saiago, C. (2009), Álgebra linear, Escolar. -- Anton, H., Busby, R. (2006), Álgebra Linear Contemporânea, Bookman. -- Dias Agudo, F. R. (1992), Introdução à Álgebra Linear e Geometria Analítica, Escolar. -- Lay, D. C. (2005), Álgebra Linear e suas aplicações, LTC. -- Lay, D. C. (2012), Linear Algebra and its Applications, Pearson. -- Magalhães, L. T. (2001), Álgebra linear como introdução à matemática aplicada, Escolar. -- Nering, E. N. (1970), Linear Algebra And Matrix Theory, John Wiley. -- Santana, A. P., Queiró, J. (2018), Introdução à Álgebra Linear, gradiva. -- Santos, R. S. (2010), Introdução à Álgebra Linear, http://www.mat.ufmg.br/~regi/gaalt/gaalt00.pdf -- Strang, G. (1976), Linear Algebra And Its Applications, Academic. -- Takahashi, R. (2009), Projeto de Estrutura Metálica, http:// www.mat.ufmg.br/gaal/aplicacoes/estruturas_m -- Vujicic, M. (2008), Linear algebra thoroughly explained, Springer. |

Teaching Methodologies and Assessment Criteria |
1) This year there will be no minimum attendance in classes. 2) The evaluation will be carried out through the realization of 2 frequencies (1st frequency = 8 values and 2nd frequency = 12 values). 3) If the student wishes, they can take 3 DataCamp courses: Introduction to R, Intermediate R and Linear Algebra for Datascience in R. In this case, the 1st and 2nd frequencies will be worth 34% and 51% the final grade, respectively and the Datacamp15%. 4) The student obtain approval to the discipline if the Final Classification is equal to or higher than 9.5 values. 4) The student with a Final Classification higher than 17 values is conditioned to an oral exam to defend the grade. If you do not want to, you get the Final Classification of 17 values. 5) Situations not previously provided for will be resolved by the discipline's governor. Student workers can be assessed by the same mold as ordinary students or by a single frequency on the same day as the 2nd frequency. |

Language | Portuguese. Tutorial support is available in English. |