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Featuring numerous problems, along with a solutions manual for qualifying instructors, this classroom-tested text explores the fundamental ideas of linear algebra as well as a variety of applications. It discusses proofs thoroughly to show how to correctly create and write them; offers the option of using Maple(TM), MATLAB(R), and TI-83 Plus to help solve arduous problems and reinforce the learning of standard procedures; and distributes the abstract aspects of the material uniformly to promote steady student learning. Many examples of real-world applications, such as center of gravity and PageRank, make the concepts relevant and meaningful.