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The Eighth Edition of Gareth Williams' classic text is designed for the introductory linear algebra course, and provides a flexible blend of theory and engaging applications for students within engineering, science, mathematics, business management, and physics. The text's 29 core sections within 8 chapters are organized into 3 Parts: Part 1 introduces the basics, presenting systems of linear equations, vectors and subspaces of R(n), matrices, linear transformations, determinants, and eigenvectors. Part 2 builds on the material presented in Part1 and goes on to introduce the concepts of general vector spaces, discussing properties of bases, develops the rank/nullity theorem, and introduces spaces of matrices and functions.Part 3 completes the course with many of the important ideas and methods of numerical linear algebra, such as ill-conditioning, pivoting, and LU decomposition.Throughout the text the author takes care to fully and clearly develop the mathematical concepts first and then provide modern applications to reinforce those concepts. The applications range from theoretical applications within differential equations and least square analysis, to practical applications in fields such as archeology, demography, electrical engineering and more.