- 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
*A***x**=**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 R
^{n} - 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

Section 1.1 | Section 1.2 | Section 1.3 | |||
---|---|---|---|---|---|

Exercise 1 | Exercise 18 | Exercise 1 | Exercise 18 | Exercise 1 | Exercise 18 |

Exercise 2 | Exercise 19 | Exercise 2 | Exercise 19 | Exercise 2 | Exercise 19 |

Exercise 3 | Exercise 20 | Exercise 3 | Exercise 20 | Exercise 3 | Exercise 20 |

Exercise 4 | Exercise 21 | Exercise 4 | Exercise 21 | Exercise 4 | Exercise 21 |

Exercise 5 | Exercise 22 | Exercise 5 | Exercise 22 | Exercise 5 | Exercise 22 |

Exercise 6 | Exercise 23 | Exercise 6 | Exercise 23 | Exercise 6 | Exercise 23 |

Exercise 7 | Exercise 24 | Exercise 7 | Exercise 24 | Exercise 7 | Exercise 24 |

Exercise 8 | Exercise 25 | Exercise 8 | Exercise 25 | Exercise 8 | Exercise 25 |

Exercise 9 | Exercise 26 | Exercise 9 | Exercise 26 | Exercise 9 | Exercise 26 |

Exercise 10 | Exercise 27 | Exercise 10 | Exercise 27 | Exercise 10 | Exercise 27 |

Exercise 11 | Exercise 28 | Exercise 11 | Exercise 28 | Exercise 11 | Exercise 28 |

Exercise 12 | Exercise 29 | Exercise 12 | Exercise 29 | Exercise 12 | Exercise 29 |

Exercise 13 | Exercise 30 | Exercise 13 | Exercise 30 | Exercise 13 | Exercise 30 |

Exercise 14 | Exercise 31 | Exercise 14 | Exercise 31 | Exercise 14 | Exercise 31 |

Exercise 15 | Exercise 32 | Exercise 15 | Exercise 32 | Exercise 15 | Exercise 32 |

Exercise 16 | Exercise 33 | Exercise 16 | Exercise 33 | Exercise 16 | Exercise 33 |

Exercise 17 | Exercise 34 | Exercise 17 | Exercise 34 | Exercise 17 | Exercise 34 |

Section 1.4 | Section 1.5 | Section 1.6 | Section 1.7 | |||
---|---|---|---|---|---|---|

Exercise 1 | Exercise 23 | Exercise 1 | Exercise 23 | Exercise 1 | Exercise 1 | Exercise 23 |

Exercise 2 | Exercise 24 | Exercise 2 | Exercise 24 | Exercise 2 | Exercise 2 | Exercise 24 |

Exercise 3 | Exercise 25 | Exercise 3 | Exercise 25 | Exercise 3 | Exercise 3 | Exercise 25 |

Exercise 4 | Exercise 26 | Exercise 4 | Exercise 26 | Exercise 4 | Exercise 4 | Exercise 26 |

Exercise 5 | Exercise 27 | Exercise 5 | Exercise 27 | Exercise 5 | Exercise 5 | Exercise 27 |

Exercise 6 | Exercise 28 | Exercise 6 | Exercise 28 | Exercise 6 | Exercise 6 | Exercise 28 |

Exercise 7 | Exercise 29 | Exercise 7 | Exercise 29 | Exercise 7 | Exercise 7 | Exercise 29 |

Exercise 8 | Exercise 30 | Exercise 8 | Exercise 30 | Exercise 8 | Exercise 8 | Exercise 30 |

Exercise 9 | Exercise 31 | Exercise 9 | Exercise 31 | Exercise 9 | Exercise 9 | Exercise 31 |

Exercise 10 | Exercise 32 | Exercise 10 | Exercise 32 | Exercise 10 | Exercise 10 | Exercise 32 |

Exercise 11 | Exercise 33 | Exercise 11 | Exercise 33 | Exercise 11 | Exercise 11 | Exercise 33 |

Exercise 12 | Exercise 34 | Exercise 12 | Exercise 34 | Exercise 12 | Exercise 12 | Exercise 34 |

Exercise 13 | Exercise 35 | Exercise 13 | Exercise 35 | Exercise 13 | Exercise 13 | Exercise 35 |

Exercise 14 | Exercise 36 | Exercise 14 | Exercise 36 | Exercise 14 | Exercise 14 | Exercise 36 |

Exercise 15 | Exercise 37 | Exercise 15 | Exercise 37 | Exercise 15 | Exercise 37 | |

Exercise 16 | Exercise 38 | Exercise 16 | Exercise 38 | Exercise 16 | Exercise 38 | |

Exercise 17 | Exercise 39 | Exercise 17 | Exercise 39 | Exercise 17 | Exercise 39 | |

Exercise 18 | Exercise 40 | Exercise 18 | Exercise 40 | Exercise 18 | Exercise 40 | |

Exercise 19 | Exercise 41 | Exercise 19 | Exercise 19 | Exercise 41 | ||

Exercise 20 | Exercise 42 | Exercise 20 | Exercise 20 | Exercise 42 | ||

Exercise 21 | Exercise 21 | Exercise 21 | Exercise 43 | |||

Exercise 22 | Exercise 22 | Exercise 22 | Exercise 44 |

Section 1.8 | Section 1.9 | Section 1.10 | Ch. 1 SE | |||
---|---|---|---|---|---|---|

Exercise 1 | Exercise 21 | Exercise 1 | Exercise 21 | Exercise 1 | Exercise 1 | Exercise 21 |

Exercise 2 | Exercise 22 | Exercise 2 | Exercise 22 | Exercise 2 | Exercise 2 | Exercise 22 |

Exercise 3 | Exercise 23 | Exercise 3 | Exercise 23 | Exercise 3 | Exercise 3 | Exercise 23 |

Exercise 4 | Exercise 24 | Exercise 4 | Exercise 24 | Exercise 4 | Exercise 4 | Exercise 24 |

Exercise 5 | Exercise 25 | Exercise 5 | Exercise 25 | Exercise 5 | Exercise 5 | Exercise 25 |

Exercise 6 | Exercise 26 | Exercise 6 | Exercise 26 | Exercise 6 | Exercise 6 | |

Exercise 7 | Exercise 27 | Exercise 7 | Exercise 27 | Exercise 7 | Exercise 7 | |

Exercise 8 | Exercise 28 | Exercise 8 | Exercise 28 | Exercise 8 | Exercise 8 | |

Exercise 9 | Exercise 29 | Exercise 9 | Exercise 29 | Exercise 9 | Exercise 9 | |

Exercise 10 | Exercise 30 | Exercise 10 | Exercise 30 | Exercise 10 | Exercise 10 | |

Exercise 11 | Exercise 31 | Exercise 11 | Exercise 31 | Exercise 11 | Exercise 11 | |

Exercise 12 | Exercise 32 | Exercise 12 | Exercise 32 | Exercise 12 | Exercise 12 | |

Exercise 13 | Exercise 33 | Exercise 13 | Exercise 33 | Exercise 13 | Exercise 13 | |

Exercise 14 | Exercise 34 | Exercise 14 | Exercise 34 | Exercise 14 | Exercise 14 | |

Exercise 15 | Exercise 35 | Exercise 15 | Exercise 35 | Exercise 15 | ||

Exercise 16 | Exercise 36 | Exercise 16 | Exercise 36 | Exercise 16 | ||

Exercise 17 | Exercise 37 | Exercise 17 | Exercise 37 | Exercise 17 | ||

Exercise 18 | Exercise 38 | Exercise 18 | Exercise 38 | Exercise 18 | ||

Exercise 19 | Exercise 39 | Exercise 19 | Exercise 39 | Exercise 19 | ||

Exercise 20 | Exercise 40 | Exercise 20 | Exercise 40 | Exercise 20 |