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.