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This text achieves a balance among computational skills, theories and applications of linear algebra. The contents can be arranged to allow for the presentation of a traditional introduction to linear algebra or a more applied course. More than 330 solved examples are included; many are computational and devoted to applications. This edition leans towards matrix computations and applications, and has a much less abstract focus than the second edition. This fifth edition has been updated to include: emphasis on more matrix computation with a corresponding lowering of the level of absraction; new exercises and examples; new sections on positive definitive matrices and the block upper triangular form of a matrix; sections on Gaussian elimination and vector geometry; Eigenvalues and diagonalization with applications moved earlier in text (chapter 6); removal of chapter 9 with discussion of operators being divided between chapters 7 and 8; biographical footnotes.