A large number of exercises have been added to the problem sets, from the elementary to the challenging and from the abstract to the applied. For example, there are quite a few new exercises on “Fibonacci Matrices” and their eigenvectors and eigenvalues. Throughout the text, the author added an ongoing discussion of the mathematical principles behind search engines—and the notion of PageRank in particular—with dozens of examples and exercises. Besides being an interesting and important contemporary application of linear algebra, this topic allows for an early and meaningful introduction to dynamical systems, one of the main themes of this text, naturally leading up to a discussion of diagonalization and eigenvectors. A new appendix offers a brief discussion of the proof techniques of Induction and Contraposition. Hundreds of improvements, such as offering hint in a challenge problem, for example, or choosing a more sensible notation in a definition.