Lecture schedule:

Date |
Topic |
Reading to prepare for class |
Suggested practice problems |
Lecture Notes |

Thurs, Jan 4 | Linear systems + introduction to row reduction | Section 1.1 | 1.1 exercises 11-14, 15, 17, 19, 23 | Scanned Notes |

Tues, Jan 9 | Row reduction, vector equations | Sections 1.2+1.3 | 1.2 exercises 1, 3, 5, 7-11, 13, 15, 17, 21, 23 1.3 exercises 1-4, 7, 11, 17, 23 |
Scanned Notes |

Thurs, Jan 11 | Vector equations and matrix equations | Section 1.4 | 1.4 exercises 1-4, 9, 10, 11, 12, 21, 22, 23, 24 | Scanned Notes |

Tues, Jan 16 | Solution sets of linear systems, starting on applications of linear systems. | Sections 1.5-1.6 | 1.5 exercises 7-10, 13, 14, 15, 23, 24, 26, 27, 28-31, 32, 33 | Scanned Notes |

Thurs, Jan 18 | Applications of Linear Systems, starting on linear independence | Sections 1.6-1.7 | 1.6 exercises 1, 3, 7-11, 12-15 (the parts marked with an [M] are intended to be done with a calculator / math software and are optional). | Scanned Notes |

Tues, Jan 23 | Linear independence and linear transformations | Sections 1.7-1.8 | 1.7 exercises 1, 2, 5, 7, 9, 10, 15-20, 27, 28, 33-38. (Highlight to check your answers to 34, 36, 38: 34 is false, 36 is false, 38 is true) | Scanned Notes |

Thurs, Jan 25 | Linear transformations and their matrices | Sections 1.8-1.9 | 1.8 exercises 3,5,9,11,13-16,18,27,31,32-35 1.9 exercises 1-6,9,10,12,17,19,25,27,28 |
Scanned Notes |

Tues, Jan 30 | Matrix operations | Section 2.1 | 2.1 exercises 1-4, 9, 10, 12, 13, 18-21, 27 | Scanned Notes |

Thurs, Feb 1 | Inverses of matrices | Section 2.2 | 2.2 exercises 1, 3, 5, 6, 8, 12, 21-24, 31, 32, 33 | Scanned Notes |

Tues, Feb 6 | Characterizations of invertibility | Section 2.3 | 2.3 exercises 1-8, 13, 17, 21, 23, 27, 33 | Scanned Notes |

Thurs, Feb 8 | Midterm 1 |
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Tues, Feb 13 | Subspaces of R^{n} |
Section 2.5 | 2.5 exercises 1-4, 7, 9, 11-14, 23, 25, 27-29 | Scanned Notes |

Thurs, Feb 15 | Dimension and Rank | Section 2.6 | 2.6 exercises 1, 2, 3, 5, 7, 9, 11, 13, 14 | Scanned Notes |

Tues, Feb 20 | No class - midterm break |
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Thurs, Feb 22 | No class - midterm break |
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Tues, Feb 27 | A bit about coordinates; introduction to determinants | Sections 2.6 and 3.1 | Scanned Notes | |

Thurs, Mar 1 | More on determinants | Sections 3.1 and 3.2 | 3.1 exercises 9, 11, 13, 15-18, 19, 21 3.2 exercises 1-4, 4, 7, 9, 15-20, 21, 25, 29 |
Scanned Notes |

Tues, Mar 6 | Eigenvectors and eigenvalues | Section 4.1 | 4.1 exercises 1-8, 9, 11, 13, 15, 17-20 | Scanned Notes |

Thurs, Mar 8 | The characteristic equation | Section 4.2 | 4.2 exercises 1, 3, 5, 7, 9, 11, 13, 15, 17, 18 | Scanned Notes |

Tues, Mar 13 | Diagonalization | Section 4.3 | 4.3 exercises 1, 3, 5, 7, 9, 11, 15, 17, 23, 24, 27 | Scanned Notes |

Thurs, Mar 15 | Discrete dynamical systems | Section 4.6 | 4.6 exercises 1, 3-7, 15 | Scanned Notes |

Tues, Mar 20 | Finishing with eigenvectors, starting inner products | Sections 5.1-5.2 | 5.1 exercises 1, 3, 5, 7, 9, 11, 13, 15, 17, 24, 31 | Scanned Notes |

Thurs, Mar 22 | Midterm 2 |
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Tues, Mar 27 | Orthogonal sets and orthogonal projections | Sections 5.2-5.3 | 5.2 exercises 1, 3, 5, 7, 9, 13, 17 5.3 exercises 1, 3, 5, 11, 13, 15 |
Scanned Notes |

Thurs, Mar 29 | Orthogonal projections and the Gram-Schmidt process | Sections 5.3-5.4 | 5.4 exercises 1, 3, 5, 7, 9 | Scanned Notes |

Tues, Apr 3 | Least-squares problems | Section 5.5 | 5.5 exercises 1, 3, 5, 7, 9, 11, 13, 19, 21 | Scanned Notes |

Thurs, Apr 5 | Summary + a few final topics | Scanned Notes |

Homework schedule:

- WebWork assignment 1: Due Wednesday January 17 (posted Wednesday January 10)
- WebWork assignment 2: Due Wednesday January 24
- WebWork assignment 3: Due Wednesday January 31
- WebWork assignment 4: Due Wednesday February 14
- WebWork assignment 5: Due Wednesday February 28
- WebWork assignment 6: Due Wednesday March 7
- WebWork assignment 7: Due Wednesday March 14
- WebWork assignment 8: Due Wednesday March 28
- WebWork assignment 9: Due Wednesday April 4

The sections listed above are for the textbook for the course, the third custom UBC edition of

- 1.1 Systems of linear equations

- 1.2 Row reduction and echelon forms

- 1.3 Vector equations

- 1.4 The matrix equation Ax = b

- 1.5 Solution sets of linear equations

- 1.6 Applications of linear systems (skip economic models)

- 1.7 Linear independence

- 1.8 Introduction to linear transformations

- 1.9 The matrix of a linear transformation

- 2.1 Matrix operations

- 2.2 The inverse of a matrix (skip elementary matrices)

- 2.3 Characterizations of invertible matrices

- 2.5 Subspaces of Rn

- 2.6 Dimension and rank

- 3.1 Introduction to determinants

- 3.2 Properties of determinants

- 4.1 Eigenvectors and eigenvalues

- 4.2 The characteristic equation

- 4.3 Diagonalization

- 4.6 Discrete dynamical systems

- 5.1 Inner product, length, and orthogonality

- 5.2 Orthogonal sets

- 5.3 Orthogonal projections

- 5.3 The Gram-Scmhidt process

- 5.5 Least-square problems