This book brings together linear algebra, numerical methods and an easy to use programming environment under Matlab (and Scilab). One of the key features of the book is the worked out examples and exercises at the end of each chapter. The reader is asked to do some numerical experiments in Matlab and then to prove the results theoretically. The book is a combination and update of two earlier French books by the authors. It is appropriate for both undergraduate and beginning graduate courses in mathematics as well as for working scientists and engineers as a self-study tool and reference. A solutions manual is available for instructors.