Hour and topic | Assignment | Relevant reading | Due date | Solutions |
---|---|---|---|---|
0. Vector and Matrix Basics | Problem Set 0 | Basics of Vectors and Matrices | W 9/6 | Solutions |
1. Introduction to Linear Systems | Problem Set 1 | Bretscher 1.1, The Method of Elimination | F 9/8 | Solutions |
Weekly Problems | ||||
2. Gauss-Jordan Elimination | Problem Set 2 | Bretscher 1.2 | M 9/11 | Solutions |
3. Introduction to Linear Transformations | Problem Set 3 | Introduction to Linear Transformations | W 9/13 | Solutions |
4. How much data do you need to determine a linear transformation? | Problem Set 4 | Linear Combinations and Linear Transformations | F 9/15 | Solutions |
5. More Examples of Linear Transformations | Problem Set 5 | Bretscher 2.2 (you may skip the formulas for projections and reflections involving dot products) | M 9/18 | Solutions |
6. More on Bases of \(\mathbb{R}^n\), Matrix Products | Problem Set 6 | Bretscher 2.3; you may skip the discussion of block matrices | W 9/20 | Solutions |
7. Matrix Inverses | Problem Set 7 | Bretscher 2.4; you may skip the part on block matrices | F 9/22 | Solutions |
8. Coordinates | Problem Set 8 | Coordinates | M 9/25 | Solutions |
9. Image and Kernel of a Linear Transformation, Introduction to Linear Independence | Problem Set 9 | Bretscher 3.1 but don't worry about the term "rank" yet; we'll talk about that next week | W 9/27 | Solutions |
10. Subspaces of \(\mathbb{R}^n\), Bases and Linear Independence | Problem Set 10 If you'd like more guidance on writing arguments showing that a set is closed under addition or scalar multiplication, check out the worksheet solutions, especially #3. |
Bretscher 3.2 | F 9/29 | Solutions |
11. Dimension and the Rank-Nullity Theorem | Problem Set 11 | Bretscher 3.3 | M 10/2 | Solutions |
12. Orthogonal Projections and Orthonormal Bases | Problem Set 12 | Bretscher 5.1 | F 10/6 | Solutions |
13. Determinants | No problem set! (This material is covered in Problem Set 15.) | Computing Determinants Using Minors; Bretscher 6.1 through Example 4; Bretscher 6.2: Theorem 6.2.1, Theorem 6.2.6, Theorem 6.2.8, Example 6 | ||
14. The Gram-Schmidt Process, The Transpose of a Matrix | Problem Set 14 | Bretscher 5.2 (skip QR factorization) and the following parts of Bretscher 5.3: from Definition 5.3.5 to Theorem 5.3.6, and Theorem 5.3.9 | W 10/11 | Solutions |
15. Least Squares and Data Fitting | Problem Set 15 | Bretscher 5.4 through Theorem 5.4.5 only | F 10/13 | Solutions |
16. Introduction to Discrete Dynamical Systems and Eigenanalysis | Problem Set 16 | §7.1 from the 4th edition of Bretscher (if you have the 5th edition, we've posted a copy here); Complex Numbers (and solutions to the practice problems) | M 10/16 | |
17. Finding the Eigenvalues and Eigenvectors of a Matrix | Problem Set 17 | Bretscher 7.2 and 7.3, but skip Theorem 7.3.6 and Example 6 in the 4th edition / Theorem 7.3.5 and Example 5 in the 5th edition; Complex Numbers (see the Handouts page for solutions to the practice problems) | W 10/18 | |
18. Diagonalization | Problem Set 18 | Bretscher 7.4 through Example 5 and Bretscher 7.5 through Example 5 if you have the 4th edition, Bretscher 7.1 and Bretscher 7.5 through Example 5 if you have the 5th edition | F 10/20 | |
19. Diagonalization, Continued | Problem Set 19 | Bretscher 7.5 | M 10/23 | |
20. Orthogonal Matrices, Symmetric Matrices and the Spectral Theorem | Problem Set 20 | Orthogonal Matrices, Symmetric Matrices and the Spectral Theorem | W 10/25 |
Note: Solutions to in-class worksheets can all be found on the worksheets page.