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__For sophomore-level orjunior/senior-level first courses in linear algebra; assumes calculus as aprerequisite.__ **A thorough and accessibleintroduction to linear algebra.** The new **10thEdition**of**__Linear Algebra with Applications__** continuesto encourage a challenging and broad understanding of the subject. For thisedition, Steven Leon―one of the leading figures in the use of technology forlinear algebra―is joined by new co-author Lisette de Pillis of Harvey MuddCollege, who brings her passion for teaching and solving real-world problems tothis revision. Each chapter contains integratedworked examples, practical applications, computer exercises, and chapter tests. The important roles played by geometry and visualization in understandinglinear algebra are emphasized. Cover 1 Title Page 2 Copyright 3 Dedication 4 Contents 6 Preface 10 Chapter 1: Matrices and Systems of Equations 16 1.1 Systems of Linear Equations 16 1.2 Row Echelon Form 27 1.3 Matrix Arithmetic 42 1.4 Matrix Algebra 62 1.5 Elementary Matrices 76 1.6 Partitioned Matrices 86 Chapter 1 Exercises 96 MATLAB Exercises 96 Chapter Test A: True or False 100 Chapter Test B 101 Chapter 2: Determinants 102 2.1 The Determinant of a Matrix 102 2.2 Properties of Determinants 109 2.3 Additional Topics and Applications 116 Chapter 2 Exercises 124 MATLAB Exercises 124 Chapter Test A True or False 126 Chapter Test B 126 Chapter 3: Vector Spaces 127 3.1 Definition and Examples 127 3.2 Subspaces 135 3.3 Linear Independence 149 3.4 Basis and Dimension 161 3.5 Change of Basis 167 3.6 Row Space and Column Space 177 Chapter 3 Exercises 185 MATLAB Exercises 185 Chapter Test A True or False 186 Chapter Test B 187 Chapter 4: Linear Transformations 189 4.1 Definition and Examples 189 4.2 Matrix Representations of Linear Transformations 198 4.3 Similarity 213 Chapter 4 Exercises 219 MATLAB Exercises 219 Chapter Test A True or False 220 Chapter Test B 220 Chapter 5: Orthogonality 222 5.1 The Scalar Product in Rn 223 5.2 Orthogonal Subspaces 238 5.3 Least Squares Problems 246 5.4 Inner Product Spaces 259 5.5 Orthonormal Sets 268 5.6 The Gram–Schmidt Orthogonalization Process 287 5.7 Orthogonal Polynomials 296 Chapter 5 Exercises 304 MATLAB Exercises 304 Chapter Test A True or False 306 Chapter Test B 306 Chapter 6: Eigenvalues 308 6.1 Eigenvalues and Eigenvectors 309 6.2 Systems of Linear Differential Equations 324 6.3 Diagonalization 336 6.4 Hermitian Matrices 354 6.5 The Singular Value Decomposition 366 6.6 Quadratic Forms 383 6.7 Positive Definite Matrices 396 6.8 Nonnegative Matrices 404 Chapter 6 Exercises 413 MATLAB Exercises 413 Chapter Test A True or False 417 Chapter Test B 418 Chapter 7: Numerical Linear Algebra 420 7.1 Floating-Point Numbers 421 7.2 Gaussian Elimination 429 7.3 Pivoting Strategies 434 7.4 Matrix Norms and Condition Numbers 440 7.5 Orthogonal Transformations 454 7.6 The Eigenvalue Problem 465 7.7 Least Squares Problems 476 7.8 Iterative Methods 488 Chapter 7 Exercises 494 MATLAB Exercises 494 Chapter Test A True or False 499 Chapter Test B 500 Chapter 8: Canonical Forms 502 8.1 Nilpotent Operators 502 8.2 The Jordan Canonical Form 513 Appendix: MATLAB 522 Bibliography 534 Answers to Selected Exercises 537 Index 550 A 550 B 550 C 550 D 550 E 550 F 551 G 551 H 551 I 551 J 551 K 551 L 551 M 552 N 553 O 553 P 553 Q 554 R 554 S 554 T 554 U 554 V 555 W 555 X 555 Y 555 Z 555 This book is for junior/senior-level first courses in linear algebra and assumes calculus as a prerequisite. This thorough and accessible text, from one of the leading figures in the use of technology in linear algebra, gives students a challenging and broad understanding of the subject. The author infuses key concepts with their modern practical applications to offer students examples of how mathematics is used in the real world. Each chapter contains integrated worked examples and chapter tests. The book stresses the important roles geometry and visualisation play in understanding linear algebra. The full text downloaded to your computer With eBooks you can: search for key concepts, words and phrases make highlights and notes as you study share your notes with friends eBooks are downloaded to your computer and accessible either offline through the Bookshelf (available as a free download), available online and also via the iPad and Android apps. Upon purchase, you'll gain instant access to this eBook. Time limit The eBooks products do not have an expiry date. You will continue to access your digital ebook products whilst you have your Bookshelf installed. For sophomore-level orjunior/senior-level first courses in linear algebra; assumes calculus as aprerequisite. A thorough and accessibleintroduction to linear algebra.The new 10thEdition of Linear Algebra with Applications continuesto encourage a challenging and broad understanding of the subject. For thisedition, Steven Leon―one of the leading figures in the use of technology forlinear algebra―is joined by new co-author Lisette de Pillis of Harvey MuddCollege, who brings her passion for teaching and solving real-world problems tothis revision. Each chapter contains integratedworked examples, practical applications, computer exercises, and chapter tests. The important roles played by geometry and visualization in understandinglinear algebra are emphasized. For sophomore-level orjunior/senior-level first courses in linear algebra; assumes calculus as aprerequisite. A thorough and accessibleintroduction to linear algebra. The new 10thEdition of Linear Algebra with Applications continuesto encourage a challenging and broad understanding of the subject. For thisedition, Steven Leon―one of the leading figures in the use of technology forlinear algebra―is joined by new co-author Lisette de Pillis of Harvey MuddCollege, who brings her passion for teaching and solving real-world problems tothis revision. Each chapter contains integratedworked examples, practical applications, computer exercises, and chapter tests. The important roles played by geometry and visualization in understandinglinear algebra are emphasized.