LinAlg_Complete

# LinAlg_Complete - LINEAR ALGEBRA Paul Dawkins Linear...

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Unformatted text preview: LINEAR ALGEBRA Paul Dawkins Linear Algebra © 2007 Paul Dawkins i Table of Contents Preface . ........................................................................................................................................... ii Outline . .......................................................................................................................................... iii Systems of Equations and Matrices . ............................................................................................ 1 Introduction . ............................................................................................................................................... 1 Systems of Equations . ................................................................................................................................ 3 Solving Systems of Equations . ................................................................................................................. 15 Matrices . ................................................................................................................................................... 27 Matrix Arithmetic & Operations . ............................................................................................................. 33 Properties of Matrix Arithmetic and the Transpose . ................................................................................ 45 Inverse Matrices and Elementary Matrices . ............................................................................................. 50 Finding Inverse Matrices. ......................................................................................................................... 59 Special Matrices . ...................................................................................................................................... 68 LU-Decomposition . .................................................................................................................................. 75 Systems Revisited . ................................................................................................................................... 81 Determinants . ............................................................................................................................... 90 Introduction . ............................................................................................................................................. 90 The Determinant Function . ...................................................................................................................... 91 Properties of Determinants . ..................................................................................................................... 100 The Method of Cofactors . ....................................................................................................................... 107 Using Row Reduction To Compute Determinants . Using Row Reduction To Compute Determinants ....
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