Instructor's Solutions Manual for Linear Algebra and Its Applications, Global Edition

Table of Contents:
1. Linear Equations in LinearAlgebra Introductory Example: LinearModels in Economics and Engineering 1.1 Systems of Linear Equations 1.2 Row Reduction and EchelonForms 1.3 Vector Equations 1.4 The Matrix Equation Ax= b 1.5 Solution Sets of LinearSystems 1.6 Applications of Linear Systems 1.7 Linear Independence 1.8 Introduction to LinearTransformations 1.9 The Matrix of a LinearTransformation 1.10 Linear Models in Business,Science, and Engineering Projects Supplementary Exercises   2. Matrix Algebra Introductory Example: ComputerModels in Aircraft Design 2.1 Matrix Operations 2.2 The Inverse of a Matrix 2.3 Characterizations ofInvertible Matrices 2.4 Partitioned Matrices 2.5 Matrix Factorizations 2.6 The Leontief Input—OutputModel 2.7 Applications to ComputerGraphics 2.8 Subspaces of ℝn 2.9 Dimension and Rank Projects Supplementary Exercises   3. Determinants Introductory Example: Random Pathsand Distortion 3.1 Introduction to Determinants 3.2 Properties of Determinants 3.3 Cramer’s Rule, Volume, andLinear Transformations Projects Supplementary Exercises   4. Vector Spaces Introductory Example: Space Flightand Control Systems 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 VectorSpace 4.6 Change of Basis 4.7 Digital Signal Processing 4.8 Applications to DifferenceEquations Projects Supplementary Exercises   5. Eigenvalues and Eigenvectors Introductory Example: DynamicalSystems and Spotted Owls 5.1 Eigenvectors and Eigenvalues 5.2 The Characteristic Equation 5.3 Diagonalization 5.4 Eigenvectors and LinearTransformations 5.5 Complex Eigenvalues 5.6 Discrete Dynamical Systems 5.7 Applications to DifferentialEquations 5.8 Iterative Estimates forEigenvalues 5.9 Markov Chains Projects Supplementary Exercises   6. Orthogonality and Least Squares Introductory Example: The NorthAmerican Datum and GPS Navigation 6.1 Inner Product, Length, andOrthogonality 6.2 Orthogonal Sets 6.3 Orthogonal Projections 6.4 The Gram—Schmidt Process 6.5 Least-Squares Problems 6.6 Machine Learning and LinearModels 6.7 Inner Product Spaces 6.8 Applications of Inner ProductSpaces Projects Supplementary Exercises   7. Symmetric Matrices andQuadratic Forms Introductory Example: MultichannelImage Processing 7.1 Diagonalization of SymmetricMatrices 7.2 Quadratic Forms 7.3 Constrained Optimization 7.4 The Singular ValueDecomposition 7.5 Applications to ImageProcessing and Statistics Projects Supplementary Exercises   8. The Geometry of Vector Spaces Introductory Example: The PlatonicSolids 8.1 Affine Combinations 8.2 Affine Independence 8.3 Convex Combinations 8.4 Hyperplanes 8.5 Polytopes 8.6 Curves and Surfaces Projects Supplementary Exercises   9. Optimization Introductory Example: The BerlinAirlift 9.1 Matrix Games 9.2 Linear Programming–GeometricMethod 9.3 Linear Programming–SimplexMethod 9.4 Duality Projects Supplementary Exercises   10. Finite-State Markov Chains(Online Only) Introductory Example: GooglingMarkov Chains 10.1 Introduction and Examples 10.2 The Steady-State Vector andGoogle's PageRank 10.3 Communication Classes 10.4 Classification of States andPeriodicity 10.5 The Fundamental Matrix 10.6 Markov Chains and BaseballStatistics   Appendices A. Uniqueness of the ReducedEchelon Form B. Complex Numbers