Intended as a first and elementary introduction to linear algebra and matrix theory, this text emphasizes the computational and practical aspects of the subject. At the same time it provides a thorough and rigorous introduction to the subject at a level suitable for use in the introduction of abstract concepts in mathematics. The book is structured to cover the more concrete and practical aspects first, leading naturally to the more abstract ideas developed later. The second edition includes more examples of an analytical nature. The final section on applications to analytical geometry has been extended and some sections have been altered to improve their clarity. Numerous exercises are included in each section, with answers at the end of the book. This book should be of interest to first and second year undergraduate students of mathematics, engineering and science.