This classic treatment of linear algebra presents the fundamentals in the clearest possible way, examining basic ideas by means of computational examples and geometrical interpretation. It proceeds from familiar concepts to the unfamiliar, from the concrete to the abstract. Readers consistently praise this outstanding text for its expository style and clarity of presentation. The applications version features a wide variety of interesting, contemporary applications. This book contains clear, accessible, step-by-step explanations that make the material crystal clear. It establishes the intricate thread of relationships between systems of equations, matrices, determinants, vectors, linear transformations and eigenvalues.