## Linear algebra

### Teaching unit

### Description

### Objectives

Ability to build and develop logical arguments with a clear identification of hypotheses and conclusions.

Ability to detect inconsistencies

Know what a mathematical test is and its differences with other types of reasoning. Understand and correctly apply different types of mathematical arguments: principle of mathematical induction, reduction to the absurd, reciprocal theorem, etc.

Capacity for abstraction, including the logical development of mathematical theories and the relationships between them.

Ability to formulate problems in mathematical language, in a way that facilitates their analysis and solution.

Ability to present mathematical reasoning and its conclusions clearly and accurately and in an appropriate manner for the audience to which they are addressed, both orally and in writing.

### Subjects

#### Lecture topics

- Matrix, Matrix Operations
- Row transformations. Elementary Matrices
- Gauss-Jordan algorithm
- Inverse of a square matrix
- Determinants. Properties
- LU factorization
- Linear applications
- Overdetermined systems
- Linear fit
- Exponential fit

#### Laboratory topics

- Mathematical assistants
- Practice of linear and exponential fit