1/12-1/16

Linear systems and Gauss-Jordan elimination

Bretscher 1.1-1.2

1.1 #4, 10, 31.

1/23

1/16-1/26 (no class 1/19)

Vectors and Matrices

1.3 and 1st part of Appendix A

1.3 #1, 4, 5, 8, 12, 18, 22, 24, 28, 29 (Hint), 30 (Hint), 34, 36, 46 (explain), 55 (explain), 61 (explain).

1/30

Most of these problems have fairly short answers---often just one or two lines. The key thing is to understand the question before answering it. This might require you to look back at the definitions of various terms (like `rank' or `linear combination', etc) in order to proceed.

3Blue1Brown is an excellent Youtube channel for math. Among other things, it has a series of videos about linear algebra , including one about vectors. It also has a series about machine learning.

1/26-1/30

2.1 Linear transformations

2.1

2.1 #1, 2, 3, 5, 6, 8 (Hint), 10, 15 (Hint), 18, 19, 20, 33 (Hint), 38 (Hint), 43

2/6

Here's a nice online app that helps visualize linear transformations from R² to R². Here's another featuring the Mona Lisa.

2/2-2/6

2.2 Geometric transformations

2nd part of Appendix A and 2.2

2.2 #1, 2, 5 (Hint), 6, 7, 10, 11, 14 (Hint), 15 (Hint), 19, 20, 23 (Hint), 30, 31

2/13

2/9-2/16

2.3 Matrix products and 2.4 Matrix inverses

2.3 and 2.4

2.3 #2, 3, 10, 29, 32 (Hint), 34, 44, 61 (Hint), 62 (Hint)

2.4 #2, 6, 8, 16, 17, 18

2/20

2/18-2/20, 2/27

Image and kernel

3.1

1, 5, 10, 15, 20, 24, 25, 31 (Hint), 32, 34, 37, 44, 49

3/6

2/23

review

First midterm is Wednesday, February 25. See the webpage for a practice exam.

2/25

Exam 1

Covers through Chapter 2

2/27-3/6

Subspaces, basis, linear independence

3.2

2, 6, 8, 9, 14, 17, 30, 34, 36, 37, 39, 43, 46, 52

3/20

3/9-3/13

Spring Break

3/16-3/20

Dimension

3.3

5, 18, (Hint), 21, 22, 30 (Hint), 31, 33, 36 (Hint), 39 (Hint), 62, 67, 80, 81 (Hint)

3/27

3/23 - 3/30

Coordinates

3.4

Hints for selected problems

13, 17, 25, 27, 30, 37, 38, 40, 44, 46, 47, 56, 59, 60

4/10

Start Orthogonal projection and the Gram-Schmidt algorithm

5.1, 5.2

Continue Orthogonal projection and the Gram-Schmidt algorithm

Note that I skipped over QR decomposition of matrices. Just not enough time...

Matrix Transposes

5.3

Least squares Solutions of Linear Systems

5.4

Determinants

6.1-6.2

My take on determinants--particularly the way I order my discussion--will be different than Bretscher's. I'll use his Theorem 6.2.3 and the relationship with volume as my starting point. And I'll skip his discussion of `patterns' in 6.1.

Exam 2 on Wednesday, April 22

Cramer's Rule, volume

6.3

Eigenvalues, eigenvectors and diagonalization

7.1-7.3

Applications of diagonalization

7.4

Etc...

etc...

etc.