Linear Algebra and Analytical Geometry

Academic year
Subject Area
Language of Instruction
Other Languages of Instruction
Mode of Delivery
ECTS Credits
1st Cycle Studies

Recommended Prerequisites

Mathematics A from the Portuguese High School Curriculum.

Teaching Methods

The teaching in this course assumes two formats: theoretical and example classes. During a theoretical class teaching is mostly expository. During an example class teaching consists of problem solving by the students under the guidance of the lecturer. A strong interaction between notions and their practical application is emphasised. In this task, the visualization and the analysis of concrete examples takes on a central role and prepares the way for the abstract definitions. Tutorial support is available to students to help them on the tasks assigned by the lecturers.

Learning Outcomes

The student who successfully completes this course will be able to:
1. Solve and classify linear systems using Gauss elimination and matrix operations;
2. Compute 2 by 2 and 3 by 3 determinants and expand any determinant using the Laplace expansion;
3. Study the invertibility of a matrix using the rank or the determinant;
4. Compute the inverse of a matrix of order 2 or 3 using the Gauss-Jordan method;
5. Compute a basis and the dimension of a subspace in Rn and apply the Gram-Schmidt orthonormalisation process;
6. Use the method of least squares to determine approximate solutions of linear systems;
7. Compute eigenvalues and eigenvectors and determine whether a given matrix is diagonalisable;
8. Apply the acquired knowledge to solving problems in science and engineering.

Work Placement(s)



1. Matrices and Linear Systems
2. Determinants
3. Vector Spaces and Linear Transformations
4. Vector Spaces with an Inner Product
5. Eigenvalues and Eigenvectors. Matrix Diagonalisation
6. Applications.

Head Lecturer(s)

Ana Paula Jacinto Santana Ramires

Assessment Methods

Continuous assessment
2 or more midterm exams: 100.0%

Final assessment
Exam: 100.0%


[1] Ana Paula SANTANA, João QUEIRÓ (2010). Introdução à Álgebra Linear. Trajectos Ciência, 10. Gradiva.
[2] Luís T. MAGALHÃES (1989). Álgebra Linear como Introdução a Matemática Aplicada. Texto Editora.
[3] Chris RORRES, Howard ANTON (2014). Elementary linear algebra with supplemental applications, international student version, Hoboken, NJ: John Wiley & Sons, 11ª ed.
[4] David R. HILL e Bernard KOLMAN (2013). Álgebra Linear com Aplicações, Livros Téc. e Cient. Editora, 9ª ed.
[5] Gilbert STRANG (1988). Linear Algebra and its Applications, San Diego: Harcout Brace Jovanovich.