This book introduces interested readers, practitioners, and researchers to Mathematica methods for solving practical problems in linear algebra. It contains step-by-step solutions of problems in computer science, economics, engineering, mathematics, statistics, and other areas of application. Each chapter contains both elementary and more challenging problems, grouped by fields of application, and ends with a set of exercises. Selected answers are provided in an appendix. The book contains a glossary of definitions and theorem, as well as a summary of relevant Mathematica tools. Applications of Linear Algebra can be used both in laboratory sessions and as a source of take-home problems and projects. This book concentrates on problem solving and aims to increase the readers' analytical skills. It provides ample opportunities for applying theoretical results and transferring knowledge between different areas of application; Mathematica plays a key role in this process. It makes learning fun and builds confidence. It allows readers to tackle computationally challenging problems by minimizing the frustration caused by the arithmetic intricacies of numerical linear algebra.