## Course Summary

This is a first course in linear algebra. It is truly surprising how ubiquitous linear algebra is throughout math and sciences: from cryptography to graph theory, from machine learning to research mathematics. Whether you are an aspiring computer scientist, mathematician, physicist, biologist or engineer, the techniques we will learn in this class are a fundamental component of your studies. Topics include solving linear systems of equations, span and linear independence of vectors, linear transformations, inverses, subspaces, change of basis, the determinant function, eigenvalues and eigenvectors, and diagonalization.

## Information

**Instructor:** Josh Southerland

**Office Hours:**

- Tuesday 5:30-6:30 PDL C552
- Thursday 5:30-6:30 CMU B-006

**Office:** Padelford (PDL), C-552

**Contact:** j s o u t h e r AT u w . e d u

Additional help is available outside of class and office hours at CLUE. Visit their website to find out more about drop-in hours and dedicated M308 days.

## Homework & Webassign

For homework, you will need to use Webassign. Professor Taggart how generously typed up instructions for how to use Webassign. You can find them here. When you log into Webassign, use this link (or google "uw Webassign" to get this page).

## Exams

**Midterm 1:** Friday, January 31

**Midterm 2:** Friday, February 21

**Final Exam:** Monday, March 16

## Lecture Notes

- Lecture 1: 1.1
- Lecture 2: 1.2
- Lecture 3: 2.1
- Lecture 4: 2.2
- Lecture 5: 2.3
- Lecture 6: 3.1
- Lecture 7: 3.2
- Lecture 8: 3.3
- Lecture 9: 4.1
- Lecture 10: 4.2
- Lecture 11: 4.3
- Lecture 12: 4.4
- Lecture 13: 5.1, 5.2
- Lecture 14: 6.1
- Lecture 15: 6.2

## Exam Archives & Concept Checklists

#### Midterm 1

- Midterm 1 Concept Checklist
- Archive 1 (You may ignore all problems asking about linear transformations.)
- Archive 2 (You may ignore all problems asking about linear transformations.)
- Midterm 1 Fall 2019
- Midterm 1 Fall 2019 Solutions

#### Midterm 2

- Midterm 2 Concept Checklist
- Archive 1 (You may ignore questions asking you to change the basis, compute a determinant, or compute eigen-anything.)
- Midterm 2 Fall 2019
- Midterm 2 Fall 2019 Solutions

Final Exam: Archive 1, Archive 2 (You may ignore problems that ask about orthogonality and least squares regression. You do not need to worry about complex-valued eigenvalues, you only need to know how to work with real-valued eigenvalues.)

## Other Materials

- Chapter 1 Conceptual Problems
- Chapter 2 Conceptual Problems
- Chapter 3 Conceptual Problems
- Chapter 4 Conceptual Problems
- Chapter 5 Conceptual Problems
- Chapter 6 Conceptual Problems
- Chapter 2 Videos: Vectors, Span and Linear Independence
- Chapter 3 Videos: Linear Transformations and Matrices, Matrix Multiplication as Composition, 3D Linear Transformations
- Chapter 4 Videos: Inverse Matrices, Column Space and Null Space, Nonsquare matrices as Transformations between Dimensions, Change of Basis NOTE: If you hear references to the "determinant being non-zero", just think the matrix is invertible, or that the matrix must have linearly independent column vectors.
- Chapter 5 Video: The Determinant
- Chapter 6 Video: Eigenvalues and Eigenvectors
- Cross Product Review (Loveless)
- Scalar Equation of a Plane

## Course Schedule

Week | Monday | Tuesday | Wednesday | Thursday | Friday |
---|---|---|---|---|---|

Jan 6 | Lecture: 1.1 | Lecture: 1.1, 1.2 | Lecture: 1.2 | ||

Jan 13 | Lecture: 1.2, 2.1 | HW: 1.1, 1.2 | Lecture: 2.1 | Lecture: 2.2 | |

Jan 20 | Holiday | HW: 2.1 | Lecture: 2.3 | HW: 2.2, 2.3(Sun) | Lecture: 2.3 |

Jan 27 | Lecture: 3.1 | Review (TBD) | Lecture: 3.1, 3.2 | Review (TBD) | Midterm 1 |

Feb 3 | Lecture: 3.2 | HW: 3.1 | Lecture: 3.2, 3.3 | HW: 3.2 | Lecture: 3.3 |

Feb 10 | Lecture: 4.1 | HW: 3.3 | Lecture: 4.2 | HW: 4.1, 4.2 + 4.3 (Sun) | Lecture: 4.3 |

Feb 17 | Holiday | Review (TBD) | Lecture: Review | Review: Questions | Midterm 2 |

Feb 24 | Lecture: 4.4 | HW: 4.4 | Lecture: 5.1/5.2 | HW: 5.1 | Lecture: 5.1/5.2, 6.1 |

Mar 2 | Lecture: 6.1 | HW: 5.2 | Lecture: 6.2 | HW: 6.1 | Lecture: 6.2 |

Mar 9 | Review | HW: 6.2 | Review | Review | |

Mar 16 | Final Exam |