Student study guide, Linear algebra and its applications, fifth edition, David C. Lay, University of Maryland, Steven R. Lay, Lee University, Judi J. McDonald, Washington State University

By: McDonald, JudithContributor(s): Lay, Steven R | Lay, David CMaterial type: TextTextPublication details: Boston : Pearson, [2016] ©2016Description: various pagination illustrationsISBN: 9780321982575 ; 0321982576Subject(s): Algebras, Linear -- Study guides | Algebras, LinearDDC classification: 512.5
Contents:
ch. 1. Linear Equations in Linear Algebra -- 1.1. Systems of Linear Equations -- 1.2. Row Reduction and Echelon Forms -- 1.3. Vector Equations -- 1.4. The Matrix Equations Ax=b -- 1.5. Solution Sets of Linear Systems -- 1.6. Applications of Linear Systems -- 1.7. Linear Independence -- 1.8. Introduction to Linear Transformations -- 1.9. Matrix of a Linear Transformation -- 1.10. Linear Models in Business, Science, and Engineering -- Supplementary Exercises -- Glossary Checklist -- ch. 2. Matrix Algebra -- 2.1. Matrix Operations -- 2.2. The Inverse of a Matrix -- 2.3. Characterization of Invertible Matrices -- 2.4. Partitioned Matrices -- 2.5. Matrix Factorizations -- 2.6. The Leontief Input-Output Model -- 2.7. Applications to Computer Graphics -- 2.8. Subspaces of Rn -- 2.9. Dimension and Rank -- Supplementary Exercises -- Glossary Checklist -- ch. 3. Determinants -- 3.1. Introduction to Determinants -- 3.2. Properties of Determinants -- 3.3. Cramer's Rule, Volume and Linear Transformations -- Glossary Checklist -- ch. 4. Vector Spaces -- 4.1. Vector Spaces and Subspaces -- 4.2. Null Spaces, Column Spaces, and Linear Transformations -- 4.3. Linearly Independent Sets; Bases -- 4.4. Coordinate Systems -- 4.5. The Dimension of a Vector Space -- 4.6. Rank -- 4.7. Change of Basis -- 4.8. Applications to Difference Equations -- 4.9. Applications to Markov Chains -- Glossary Checklist -- ch. 5. Eigenvalues and Eigenvectors -- 5.1. Eigenvectors and Eigenvalues -- 5.2. The Characteristic Equation -- 5.3. Diagonalization -- 5.4. Eigenvectors and Linear Transformations -- 5.5.Complex Eigenvalues -- 5.6. Discrete Dynamical Systems -- 5.7. Applications to Differential Equations -- 5.8. Iterative Estimates for Eigenvalues -- Glossary Checklist -- ch. 6. Orthogonality and Least Squares -- 6.1. Inner Product, Length, and Orthogonality -- 6.2. Orthogonal Sets -- 6.3. Orthogonal Projections -- 6.4. The Gram-Schmidt Process -- 6.5. Least-Squares Problems -- 6.6. Applications to Linear Models -- 6.7. Inner Product Spaces -- 6.8. Applications of Inner Product Spaces -- Glossary Checklist -- ch. 7. Symmetric Matrices and Quadratic Forms -- 7.1. Diagonalization of Symmetric Matrices -- 7.2. Quadratic Forms -- 7.3. Constrained Optimization -- 7.4. The Singular Value Decomposition -- 7.5. Applications to Image Processing and Statistics -- Supplementary Exercises -- Glossary Checklist -- ch. 8. The Geometry of Vector Spaces -- 8.1. Affine Combinations -- 8.2. Affine Independence -- 8.3. Convex Combinations -- 8.4. Hyperplanes -- 8.5. Polytopes -- 8.6. Curves and Surfaces -- Glossary Checklist -- TECHNOLOGY INDEX OF PROCEDURES AND TERMS -- APPENDICES -- Introduction TO MATLAB -- Getting Started With Matlab -- Script M-Files -- Index of Matlab Commands -- Notes For the Maple Computer Algebra System -- Getting Started With Maple -- Study Guide Notes -- Index of Maple Commands -- Notes For the Mathematica Computer Algebra System -- Getting Started With Mathematica -- Study Guide Notes -- Index of Mathematica Commands -- Notes For the TI-83+/84+/89 Graphic Calculators -- Getting Started with a TI-83+ Calculator -- Getting Started with a TI-84+ Calculator -- Getting Started with a TI-89 Calculator -- Study Guide Notes -- Index of TI-84 Family Commands --Index of TI-89 Commands.
Summary: An integral part of this text, the Study Guide incorporates detailed solutions to every third odd-numbered exercise, as well as solutions to every odd-numbered writing exercise for which the main text only provides a hint.
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ch. 1. Linear Equations in Linear Algebra --
1.1. Systems of Linear Equations --
1.2. Row Reduction and Echelon Forms --
1.3. Vector Equations --
1.4. The Matrix Equations Ax=b --
1.5. Solution Sets of Linear Systems --
1.6. Applications of Linear Systems --
1.7. Linear Independence --
1.8. Introduction to Linear Transformations --
1.9. Matrix of a Linear Transformation --
1.10. Linear Models in Business, Science, and Engineering --
Supplementary Exercises --
Glossary Checklist --
ch. 2. Matrix Algebra --
2.1. Matrix Operations --
2.2. The Inverse of a Matrix --
2.3. Characterization of Invertible Matrices --
2.4. Partitioned Matrices --
2.5. Matrix Factorizations --
2.6. The Leontief Input-Output Model --
2.7. Applications to Computer Graphics --
2.8. Subspaces of Rn --
2.9. Dimension and Rank --
Supplementary Exercises --
Glossary Checklist --
ch. 3. Determinants --
3.1. Introduction to Determinants --
3.2. Properties of Determinants --
3.3. Cramer's Rule, Volume and Linear Transformations --
Glossary Checklist --
ch. 4. Vector Spaces --
4.1. Vector Spaces and Subspaces --
4.2. Null Spaces, Column Spaces, and Linear Transformations --
4.3. Linearly Independent Sets; Bases --
4.4. Coordinate Systems --
4.5. The Dimension of a Vector Space --
4.6. Rank --
4.7. Change of Basis --
4.8. Applications to Difference Equations --
4.9. Applications to Markov Chains --
Glossary Checklist --
ch. 5. Eigenvalues and Eigenvectors --
5.1. Eigenvectors and Eigenvalues --
5.2. The Characteristic Equation --
5.3. Diagonalization --
5.4. Eigenvectors and Linear Transformations --
5.5.Complex Eigenvalues --
5.6. Discrete Dynamical Systems --
5.7. Applications to Differential Equations --
5.8. Iterative Estimates for Eigenvalues --
Glossary Checklist --
ch. 6. Orthogonality and Least Squares --
6.1. Inner Product, Length, and Orthogonality --
6.2. Orthogonal Sets --
6.3. Orthogonal Projections --
6.4. The Gram-Schmidt Process --
6.5. Least-Squares Problems --
6.6. Applications to Linear Models --
6.7. Inner Product Spaces --
6.8. Applications of Inner Product Spaces --
Glossary Checklist --
ch. 7. Symmetric Matrices and Quadratic Forms --
7.1. Diagonalization of Symmetric Matrices --
7.2. Quadratic Forms --
7.3. Constrained Optimization --
7.4. The Singular Value Decomposition --
7.5. Applications to Image Processing and Statistics --
Supplementary Exercises --
Glossary Checklist --
ch. 8. The Geometry of Vector Spaces --
8.1. Affine Combinations --
8.2. Affine Independence --
8.3. Convex Combinations --
8.4. Hyperplanes --
8.5. Polytopes --
8.6. Curves and Surfaces --
Glossary Checklist --
TECHNOLOGY INDEX OF PROCEDURES AND TERMS --
APPENDICES --
Introduction TO MATLAB --
Getting Started With Matlab --
Script M-Files --
Index of Matlab Commands --
Notes For the Maple Computer Algebra System --
Getting Started With Maple --
Study Guide Notes --
Index of Maple Commands --
Notes For the Mathematica Computer Algebra System --
Getting Started With Mathematica --
Study Guide Notes --
Index of Mathematica Commands --
Notes For the TI-83+/84+/89 Graphic Calculators --
Getting Started with a TI-83+ Calculator --
Getting Started with a TI-84+ Calculator --
Getting Started with a TI-89 Calculator --
Study Guide Notes --
Index of TI-84 Family Commands --Index of TI-89 Commands.

An integral part of this text, the Study Guide incorporates detailed solutions to every third odd-numbered exercise, as well as solutions to every odd-numbered writing exercise for which the main text only provides a hint.

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