# Linear Algebra and Analytical Geometry

**Year**

1

**Academic year**

2023-2024

**Code**

01002055

**Subject Area**

Mathematics

**Language of Instruction**

Portuguese

**Mode of Delivery**

Face-to-face

**Duration**

SEMESTRIAL

**ECTS Credits**

6.0

**Type**

Compulsory

**Level**

1st Cycle Studies

## Recommended Prerequisites

High School/Portuguese.

## Teaching Methods

Classes are of theoretical and theoretical-practical type, being of expository nature and including examples and exercises that lead the students to understand and apply the material being taught. In the theoretical-practical components problems will be solved under the guidance of the teacher.

The interaction between concepts and their geometrical visualization must be discussed. The transformation of concepts into working tools is made throughout the study of the properties of the objects being studied.

Some tutorial support will be available to help the students solving the proposed tasks.

## Learning Outcomes

Being a first formal contact with mathematical abstraction, subjects concerning the general concepts of matrix, vector space and linear transformation are motivated by examples well known by students (real and complex numbers endowed by their usual algebraic structures and functions between those structures). The mathematical tools developed in the context of such concepts are to be applied in other areas of mathematics as well as in engineering (determinants, Gauss Elimination, Least Squares approximation, diagonalization of matrices).

The course aims at developing the following skills: analysis and synthesis, organization and planning, oral and written communication, problem-solving skills. On the personal level it also allows to develop self-learning skills and independent thinking, as well as the capacity to apply theoretical knowledge.

## Work Placement(s)

No## Syllabus

1. Matrices – operations with matrices. 2. Systems of Linear Equations – Gauss Elimination. 3. Inversion of a Matrix - Gauss-Jordan Algorithm. 4. Determinants. 5. Vector Spaces. 6. Linear Transformations. 7. Inner Vector Spaces – Least Squares Approximation. 8. Diagonalization of Matrices. 9. Geometrical Applications to R2 and to R3.

## Head Lecturer(s)

Margarida Maria Lopes da Silva Camarinha

## Assessment Methods

Final Assessment

*Exam: 100.0%*

Continous Assessment

*Resolution Problems: 10.0%*

*
Mini Tests: 20.0%*

*Frequency: 70.0%*

## Bibliography

Edgar Goodaire, Linear Algebra. A Pure and Applied First Course, Prentice Hall, Pearson Education Inc. 2003

Steven J. Leon, Linear Algebra with Applications, 7ª ed., Prentice Hall, New Jersey, 2006

Luís T. Magalhães, Álgebra Linear como Introdução à Matemática Aplicada, Texto Editora, 1989

Ana Paula Santana & João Filipe Queiró, Introdução à Álgebra Linear, Gradiva, 2010

Gilbert Strang, Linear Algebra and its Applications, Harcout Brace Jovanovich, San Diego, 1988