### Chapter 1

Vectors

1.1 | The Geometry and Algebra of Vectors | Exercises | p.16 |

1.2 | Length and Angle: The Dot Product | Exercises | p.29 |

1.3 | Lines and Planes | Exercises | p.44 |

1.4 | Applications | Exercises | p.57 |

Chapter Review | p.61 |

### Chapter 2

Systems Of Linear Equations

2.1 | Introduction to Systems of Linear Equations | Exercises | p.69 |

2.2 | Direct Methods for Solving Linear Systems | Exercises | p.85 |

2.3 | Spanning Sets and Linear Independence | Exercises | p.103 |

2.4 | Applications | Exercises | p.119 |

2.5 | Iterative Methods for Solving Linear Systems | Exercises | p.138 |

Chapter Review | p.140 |

### Chapter 3

Matrices

3.1 | Matrix Operations | Exercises | p.158 |

3.2 | Matrix Algebra | Exercises | p.167 |

3.3 | The Inverse of a Matrix | Exercises | p.184 |

3.4 | The LU Factorization | Exercises | p.195 |

3.5 | Subspaces, Basis, Dimension, and Rank | Exercises | p.215 |

3.6 | Introduction to Linear Transformations | Exercises | p.229 |

3.7 | Applications | Exercises | p.256 |

Chapter Review | p.263 |

### Chapter 4

Eigenvalues And Eigenvectors

4.1 | Introduction to Eigenvalues and Eigenvectors | Exercises | p.271 |

4.2 | Determinants | Exercises | p.292 |

4.3 | Eigenvalues and Eigenvectors of n X n Matrices | Exercises | p.309 |

4.4 | Similarity and Diagonalization | Exercises | p.320 |

4.5 | Iterative Methods for Computing Eigenvalues | Exercises | p.334 |

4.6 | Applications and the Perron-Frobenius Theorem | Exercises | p.370 |

Chapter Review | p.376 |

### Chapter 5

Orthogonality

5.1 | Orthogonality in R^n | Exercises | p.387 |

5.2 | Orthogonal Complements and Orthogonal Projections | Exercises | p.398 |

5.3 | The Gram-Schmidt Process and the QR Factorization | Exercises | p.405 |

5.4 | Orthogonal Diagonalization of Symmetric Matrices | Exercises | p.418 |

5.5 | Applications | Exercises | p.440 |

Chapter Review | p.443 |

### Chapter 6

Vector Spaces

6.1 | Vector Spaces and Subspaces | Exercises | p.459 |

6.2 | Linear Independence, Basis, and Dimension | Exercises | p.474 |

6.3 | Change of Basis | Exercises | p.489 |

6.4 | Linear Transformations | Exercises | p.498 |

6.5 | The Kernel and Range of a Linear Transformation | Exercises | p.513 |

6.6 | The Matrix of a Linear Transformation | Exercises | p.530 |

6.7 | Applications | Exercises | p.547 |

Chapter Review | p.550 |

### Chapter 7

Distance And Approximation

7.1 | Inner Product Spaces | Exercises | p.563 |

7.2 | Norms and Distance Functions | Exercises | p.589 |

7.3 | Least Squares Approximation | Exercises | p.609 |

7.4 | The Singular Value Decomposition | Exercises | p.632 |

7.5 | Applications | Exercises | p.644 |

Chapter Review | p.646 |