Math 21b - Homework

Course head: Janet Chen
Course preceptor: Yu-Wen Hsu (yuwenhsu@g.harvard.edu)
Here is the homework policy in a nutshell:
• Homework must be turned in to your CA at the start of section. If you miss a class, you are responsible for getting it to your CA on time. (It's a good idea to let your CA know how you intend to do this, to avoid miscommunications.)
• Late homework is never accepted.
• Your lowest homework score will be dropped at the end of the semester. (You can earn additional homework drops by taking quizzes in problem session.)
• You are welcome to work with other students. However, you should only turn in work that you understand yourself, and that you have written up yourself and explained in your own words. Any help you receive must be acknowledged.

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.