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Linear Algebra and Analytical Geometry

Code 8620
Year 1
Semester S1
ECTS Credits 6
Workload TP(60H)
Scientific area Mathematics
Entry requirements Mathematics 12th grade
Mode of delivery Face to face
Work placements There are no work placement
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 0: Motivation for Linear Algebra

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;
Main Bibliography Boulos, P., Camargo, I. (1987), Geometria Analítica, McGraw-Hill.

Cabello, J. (2006), Álgebra Lineal, Delta.

Cabral, I., Perdigão, C., Saiago, C. (2009), Álgebra Linear, Escolar.

Dias Agudo, F. R. (1992), Introdução à Álgebra Linear e Geometria Analítica, Escolar.

Khoury, J. (s. d.), Applications to Chemistry, \url{http://aix1.uottawa.ca/~jkhoury/chemistry.htm}

Lay, D. C. (2005), Álgebra Linear e suas aplicações, LTC.

Lipschutz, S. (1972), Álgebra Linear, McGraw-Hill.

Magalhães, L. T. (1989), Álgebra Linear como introdução à matemática aplicada, Texto.

Santana, A. P., Queiró, J. (2018), Introdução à Álgebra Linear, gradiva.

Santos, R. (2010), Álgebra Linear, http://www.mat.ufmg.br/~regi/livros.html
Teaching Methodologies and Assessment Criteria The methodology is student-centered, and the student is expected, during the semester, to acquire and apply the concepts through autonomous work. In this sense, the periodic assessment, which allows the student to show the acquired skills, is paramount. More concretely, two written tests and two group tasks will take place.
Language Portuguese. Tutorial support is available in English.
Last updated on: 2021-10-15

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