This book is addressed to 3rd year high school students, but also to fellow Mathematicians (since it includes a large collection of exercises). Contains the linear algebra material provided by the new syllabus (1992-1993) for this class. It includes three chapters dealing with matrices, determinants and linear systems. At the end of each chapter there are three groups of exercises. At the end of the third chapter two more groups are included. The 4th, which contains general exercises, and the 5th which contains mixed exercises, i.e. linear algebra exercises combined with various other chapters (functions, integrals, complex numbers, analytical geometry).

Emphasis is placed on exercises unknown in the Greek literature and on subjects of various exams and competitions (French Baccalaureate , exams of the Universities of Cambridge , London , Oxford , Moscow , Bucharest , etc., G. Putnam competition, Olympiad competitions, E.M.E. competitions etc. ) .

An effort was made for an understandable presentation of the relevant theory, for a methodological confrontation of certain issues and for an originality of exercises.