Solutions to Linear Algebra and its Applications 5e by Lay

Chapter 1: Linear Equations in Linear Algebra
- Section 1.1: Systems of Linear Equations
- Section 1.2: Row Reduction and Echelon Forms
- Section 1.3: Vector Equations
- Section 1.4: The Matrix Equation Ax = b
- Section 1.5: Solution Sets of Linear Systems
- Section 1.6: Applications of Linear Systems
- Section 1.7: Linear Independence
- Section 1.8: Introduction to Linear Transformations
- Section 1.9: The Matrix of a Linear Transformation
- Section 1.10: Linear Models in Business, Science, and Engineering
Chapter 2: Matrix Algebra
- Section 2.1: Matrix Operations
- Section 2.2: The Inverse of a Matrix
- Section 2.3: Characterizations of Invertible Matrices
- Section 2.4: Partitioned Matrices
- Section 2.5: Matrix Factorizations
- Section 2.6: The Leontief Input-Output Model
- Section 2.7: Applications to Computer Graphics
- Section 2.8: Subspaces of Rⁿ
- Section 2.9: Dimension and Rank

Chapter 3: Determinants
- Section 3.1: Introduction to Determinants
- Section 3.2: Properties of Determinants
- Section 3.3: Cramer's Rule, Volume, and Linear Transformations
Chapter 4: Vector Spaces
- Section 4.1: Vector Spaces and Subspaces
- Section 4.2: Null Spaces, Column Spaces, and Linear Transformations
- Section 4.3: Linearly Independent Sets; Bases
- Section 4.4: Coordinate Systems
- Section 4.5: The Dimension of a Vector Space
- Section 4.6: Rank
- Section 4.7: Change of Basis
- Section 4.8: Applications to Difference Equations
- Section 4.9: Applications to Markov Chains
Chapter 5: Eigenvalues and Eigenvectors
- Section 5.1: Eigenvectors and Eigenvalues
- Section 5.2: The Characteristic Equation
- Section 5.3: Diagonalization
- Section 5.4: Eigenvectors and Linear Transformations
- Section 5.5: Complex Eigenvalues
- Section 5.6: Discrete Dynamical Systems
- Section 5.7: Applications to Differential Equations
- Section 5.8: Iterative Estimates for Eigenvalues

Chapter 6: Orthogonality and Least Squares
- Section 6.1: Inner Product, Length, and Orthogonality
- Section 6.2: Orthogonal Sets
- Section 6.3: Orthogonal Projections
- Section 6.4: The Gram-Schmidt Process
- Section 6.5: Least-Squares Problems
- Section 6.6: Applications to Linear Models
- Section 6.7: Inner Product Spaces
- Section 6.8: Applications of Inner Product Spaces
Chapter 7: Symmetric Matrices and Quadratic Forms
- Section 7.1: Diagonalization of Symmetric Matrices
- Section 7.2: Quadratic Forms
- Section 7.3: Constrained Optimization
- Section 7.4: The Singular Value Decomposition
- Section 7.5: Applications to Image Processing and Statistics
Chapter 8: The Geometry of Vector Spaces
- Section 8.1: Affine Combinations
- Section 8.2: Affine Independence
- Section 8.3: Convex Combinations
- Section 8.4: Hyperplanes
- Section 8.5: Polytopes
- Section 8.6: Curves and Surfaces

Exercises 1.1.1 - 1.1.32

Exercises 1.1.33 - 1.2.

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