## Matrices and determinants

### Teaching unit

### Description

Introduction to matrix algebra. elementary matrices, reduced matrices and definition of determinant of a square matrix. Fundamental properties of determinants.

### Objectives

Proficiency in the operations with vectors and matrices.

Ability to represent and solve a system of linear equations by means of matrix techniques, checking previously their nature.

Learning the fundamental subspaces of a matrix and how to calculate them.

### Subjects

#### Lecture topics

- Matrix types. Operations with matrices.
- Elementary matrices.
- Inverse of a square matrix. Gauss-Jordan algorithm.
- LU factorization.
- Rank of a matrix. Inversibility criterion for a square matrix.
- Determinant of a square matrix.
- Properties of determinants. Binet-Cauchy formula.

#### Laboratory topics

- Matrices and vectors.
- Systems of linear equations.