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It emphasizes a gradual, steady development from systems of equations and matrix representation toward deeper concepts, ensuring a relatively even difficulty level across the course. 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Company  \nReading.Massachusetts·Merlo Park.California·New YorkDon Mills.Ontario·Wokingham.England·Amsterdam·BonnSydney·Singapore·Tokyo·Madrid·San Juan·Milan·Paris  \nContents  \nPREFACE ix  \nANOTE TO STUDENTS xvi  \nISYSTEMS OF LINEAR EQUATIONS 1  \nIntroductory Example:Linear Models in Economics and Engineering 1  \n1.1 Introduction to Systems of Linear Equations 2  \n1.2 Row Reduction and Echelon Forms 13  \n1.3 Applications of Linear Systems 25Supplementary Exercises 34  \n2 VECTOR AND MATRIX EQUATIONS 37  \nIntroductory Example:Nutrition Problems 37  \n2.1 Vectors in R\"   38  \n2.2 The Equation Ax=b 48  \n2.3 Solution Sets of Linear Systems 56  \n2.4 Linear Independence .63  \n2.5 Introduction to Linear Transformations 7/  \n2.6 The Matrix of a Linear Transformation 79  \n2.7 Applications to Nutrition and Population Movement 85Supplementary Exercises 92  \n3 MATRIX ALGEBRA 95  \nIntroductory Example:Computer Graphics in Automotive Design 95  \n3.1 Matrix Operations 96  \n3.2 The Inverse o a Matrix 107  \n3.3 Characterizations of Invertible Matrices 116  \n3.4 Partitioned Matrices 121  \n3.5 Matrix Factorizations 128  \n3.6 Iterative Solutions of Linear Systems 137  \n3.7 The Leontief Input-Output Model 142  \n3.8 Applications to Computer Graphics 148Supplementary Exercises 158  \nvi CONTENTS  \n4 DETERMINANTS 161  \nIntroductory Example:Determinants in Analytic Geometry 161  \n4.1 Introduction to Determinants 162  \n4.2 Properties of Determinants 168  \n4.3 Cramer's Rule,Volume,and Linear Transformations 176Supplementary Exercises 186  \n5 VECTOR SPACES 189  \nIntroductory Example:Space Flight and Control Systems 189  \n5.1 Vector Spaces and Subspaces 190  \n5.2 Null Spaces,Column Spaces,and Linear Transformations 200  \n5.3 Linearly Independent Sets;Bases 211  \n5.4 Coordinate Systems 219  \n5.5 The Dimension of a Vector Space 229  \n5.6 Rank 235  \n5.7 Change of Basis 243  \n5.8 Applications to Difference Equations 248  \n5.9 Applications to Markov Chains 259  \nSupplementary Exercises269  \n6 EIGENYALUES AND EIGENVECTORS 271  \nIntroductory Example:Dynamical Systems and Spotted Owls 271  \n6.1 Eigenvectors and Eigenvalues 273  \n6.2 The Characteristic Equation 280  \n6.3 Diagonalization 288  \n6.4 Eigenvectors and Linear Transformations 296  \n6.5 Complex Eigenvalues 303  \n6.6 Applications to Dynamical Systems 310  \n6.7 Iterative Estimates for Eigenvalues 321  \nSupplementary Exercises 329  \n# 7 ORTHOGONALITY AND LEAST-SQUARES 331\n\nIntroductory Example:Readjusting the North American Datum 331  \n7.1 Inner Product,Length,and Orthogonalityy 333  \n7.2 Orthogonal Sets 342  \n7.3 Orthogonal Projections 352  \n7.4 The Gram-Schmidt Process 359  \n7.5 Least-Squares Problems 366  \n7.6 Applications to Linear Models 376  \nCONTENTS vii  \n3847.7 Inner Product Spaces  \n7.8 Applications of Inner Product Spaces 393Supplementary Exercises 401  \n8 SYMMETRIC MATRICES AND QUADRATIC FORMS 403  \nIntroductory Example:Multichannel Image Processing 403  \n8.1 Diagonalization of Symmetric Matrices 405  \n8.2 Quadratic Forms 411  \n8.3 Constrained Optimization 419  \n8.4 The Singular Value Decomposition 426  \n8.5 Applications to Image Processing and Statistics 435Supplementary Exercises'444  \nAPPENDICES  \nA Uniqueness of the Reduced Echelon Form A-1  \nB Complex Numbers A-3  \nGLOSSARY A-9  \nANSWERS TO ODD-NUMBERED EXERCISES A-21  \n# Preface\n\nThis text provides a modern elementary introduction to linear algebra and someof its interesting applications,accessible to students with the maturity thatshould come from successfully completing two semesters of college-level math-ematics,usually calculus.  \nThe main goal of the text is to help students master the basic concepts andskills they will use later in their careers.The topics here follow the recommen-dations of the Linear Algebra Curriculum Study Group.which were based ona careful investigation of the real needs of the students and a consensus amongprofessiona","cbCaipxQGEfKOz34","https://ap.wps.com/l/cbCaipxQGEfKOz34","pdf",16877162,511,"English","# Preface\n## Distinctive Features\n## Early Introduction of Key Concepts\n## A Modern View of Matrix Multiplication\n## Linear Transformations\n# 1 Systems of Linear Equations\n## Introduction to Systems of Linear Equations\n## Row Reduction and Echelon Forms\n## Applications of Linear Systems\n# 2 Vector and Matrix Equations\n## Vectors in R\n## The Equation Ax=b\n## Solution Sets of Linear Systems\n## Linear Independence\n## Introduction to Linear Transformations\n## The Matrix of a Linear Transformation\n## Applications to Nutrition and Population Movement\n# 3 Matrix Algebra\n## Matrix Operations\n## The Inverse of a Matrix\n## Characterizations of Invertible Matrices\n## Partitioned Matrices\n## Matrix Factorizations\n## Iterative Solutions of Linear Systems\n## The Leontief Input-Output Model\n## Applications to Computer Graphics","[{\"question\":\"What is the main goal of the text?\",\"answer\":\"To help students master fundamental concepts and skills in linear algebra that they will use later in their careers.\"},{\"question\":\"How does the text present the material over the course?\",\"answer\":\"It uses a gradual but steady development, moving from introductory examples to general principles and keeping difficulty fairly even.\"},{\"question\":\"What distinctive approach does the text take regarding matrix multiplication?\",\"answer\":\"It emphasizes a modern notation and focuses on matrix columns rather than entries, tying vector space ideas to the study of linear systems.\"}]","Linear Algebra and Its Applications - A Modern Elementary Introduction | PDF",1288]