Cours : Algèbre 2

Abstract

This manuscript, developed from the Algebra 2 course intended for first-year L.M.D.students in mathematics and computer science, presents a coherent and systematically organized exploration of the core concepts of linear algebra.The text sequentially introduces the fundamental notions of vector spaces, subspaces, linearly independent and spanning sets, as well as the concepts of basis and dimension. It then examines linear mappings, emphasizing their properties, the notions of kernel and image, operations on linear mappings, and the rank theorem. A strong connection is subsequently established between linear mappings and their matrix representations, including topics such as change-of-basis matrices, determinants, and matrix inversion. The theoretical framework is then applied to the study and solution of linear systems of equations, through classical methods such as substitution, Cramer’s rule, and the Gaussian elimination method. Each section is rich in theoretical explanations and practical examples, allowing students to develop a strong understanding of the fundamentals of linear algebra and its applications.