Matrix algebra is one of the basic pillars of applied mathematics. Matrices and systems of linear equations is the heart of matrix algebra. In this didactic unit we will review fundamental notions (definitions, operations, properties, etc.) about matrices and determinants, as well as the basic algorithm to solve systems of linear equations: the Gaussian algorithm. Knowing how to solve systems of linear equations is a relatively simple algorithmic task for a student who has studied Baccalaureate. Understanding in greater depth the nature of the solutions of a system of linear equations requires a little more effort, since we need notions such as vector subspace, linear dependence, base, dimension, etc. These concepts are also addressed, although they are not developed in an abstract way but with simple and direct definitions.