Elementary Linear Algebra (Classic Version) 2nd Edition Lawrence E. Spence-Test Bank

CHAPTER 1 MATRICES, VECTORS, AND SYSTEMS OF LINEAR EQUATIONS1

        1.1 Matrices and Vectors1

        1.2 Linear Combos, Matrix—Vector Merchandise, and Specific Matrices11

        1.3 Strategies of Linear Equations25

        1.4 Gaussian Elimination39

        1.5∗ Functions of Strategies of Linear Equations54

        1.6 The Span of a Set of Vectors64

        1.7 Linear Dependence and Linear Independence73

        Chapter 1 Consider Exercises

        Chapter 1 MATLAB Exercises

CHAPTER 2 MATRICES AND LINEAR TRANSFORMATIONS90

        2.1 Matrix Multiplication90

        2.2∗ Functions of Matrix Multiplication101

        2.3 Invertibility and Elementary Matrices117

        2.4 The Inverse of a Matrix130

        2.5∗ Partitioned Matrices and Block Multiplication141

        2.6∗ TheLUDecomposition of a Matrix147

        2.7 Linear Transformations and Matrices162

        2.8 Composition and Invertibility of Linear Transformations175

        Chapter 2 Consider Exercises

        Chapter 2 MATLAB Exercises

CHAPTER 3 DETERMINANTS192

        3.1 Cofactor Development192

        3.2 Properties of Determinants204

        Chapter 3 Consider Exercises

        Chapter 3 MATLAB Exercises

CHAPTER 4 SUBSPACES AND THEIR PROPERTIES218

        4.1 Subspaces218

        4.2 Basis and Dimension232

        4.3 The Dimension of Subspaces Associated to a Matrix245

        4.4 Coordinate Strategies254

        4.5 Matrix Representations of Linear Operators266

        Chapter 4 Consider Exercises

        Chapter 4 MATLAB Exercises

CHAPTER 5 EIGENVALUES, EIGENVECTORS, AND DIAGONALIZATION282

        5.1 Eigenvalues and Eigenvectors282

        5.2 The Attribute Polynomial291

        5.3 Diagonalization of Matrices302

        5.4∗ Diagonalization of Linear Operators314

        5.5∗ Functions of Eigenvalues323

        Chapter 5 Consider Exercises

        Chapter 5 MATLAB Exercises

CHAPTER 6 ORTHOGONALITY347

        6.1 The Geometry of Vectors347

        6.2 Orthogonal Vectors360

        6.3 Orthogonal Projections374

        6.4 Least-Squares Approximations and Orthogonal Projections388

        6.5 Orthogonal Matrices and Operators398

        6.6 Symmetric Matrices412

        6.7∗ Singular Value Decomposition425

        6.8∗ Principal Factor Analysis443

        6.9∗ Rotations ofR3 and Computer Graphics452

        Chapter 6 Consider Exercises

        Chapter 6 MATLAB Exercises

CHAPTER 7 VECTOR SPACES473

        7.1 Vector Areas and Their Subspaces473

        7.2 Linear Transformations485

        7.3 Basis and Dimension495

        7.4 Matrix Representations of Linear Operators505

          7.5Inside Product Areas517

        Chapter 7 Consider Exercises

        Chapter 7 MATLAB Exercises

APPENDICES534

A Models534

B Options536

C Sophisticated Numbers539

D Matlab544

E The Uniqueness of the Lowered Row Echelon Sort558

REFERENCES561

ANSWERS TO SELECTED EXERCISES562

LIST OF FREQUENTLY USED SYMBOLS608

INDEX609