Quizzes will be

- Quiz 1 - Tuesday January 10 (Solution)
- Material: Sections 1.1, 1.2, 1.3 from the textbook.
- Relevant problems for Section 1.1: 11-32
- Relevant problems for Section 1.2: 1-31
- Relevant problems for Section 1.3: 1-26

- Quiz 2 - Tuesday January 17 (Solution)
- Material: Sections 1.3, 1.4, 1.5 from the textbook.
- Suggested problems for Section 1.4: 1-4, 9, 10, 11, 12, 21, 22, 23, 24
- Suggested problems for Section 1.5: 7-10, 13, 14, 15, 23, 24, 26, 27, 28-31, 32, 33

- Quiz 3 - Tuesday January 24 (Solution)
- Material: Sections 1.6, 1.7 from the textbook.
- Suggested problems for Section 1.6: 1-4, 12-15 (the parts marked with an [M] are intended to be done with a calculator / math software and are optional).
- Suggested problems for Section 1.7: 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)

**Midterm 1 - Tuesday January 31**(Solution; class average was**83.6**)- Material: Sections 1.1-1.9 from the textbook (the portions covered in class).
- One practice midterm and solutions.
- A collection of practice problems (note: this is significantly longer than the actual exam will be!) and solutions (the solution to problem 13 is wrong, though, and a correct one is at here).
- Suggested problems for Section 1.8: 3,5,9,11,13-16,18,27,31,32-35
- Suggested problems for Section 1.9: 1-6,9,10,12,17,19,25,27,28

- Quiz 4 - Tuesday February 7 (Solution)
- Material: Sections 2.1 from the textbook.
- Suggested problems for Section 2.1 (Matrix Operations): 1-4, 9, 10, 12, 13, 18-21, 27

- Quiz 5 - Tuesday February 14 (Solution)
- Material: Sections 2.2-2.3 from the textbook.
- Suggested problems for Section 2.2 (Inverse of a Matrix): 1, 3, 5, 6, 8, 12, 21-24, 31, 32, 33
- Suggested problems for Section 2.3 (Characterization of Invertible Matrices): 1-8, 13, 17, 21, 23, 27, 33

- Quiz 6 - Tuesday February 28 (Solution)
- Material: Sections 2.5-2.6 from the textbook, plus coordinate system notes
- Suggested problems for Section 2.5 (Subspaces of R^n): 1-4, 7, 9, 11-14, 23, 25, 27-29
- Suggested problems for Section 2.6 (Dimension and Rank): 1, 2, 3, 5, 7, 9, 11, 13, 14
- Also suggested: The problems from the coordinate systems notes (solutions are here).

**Midterm 2 - Tuesday March 7**(Solution; the class average was**73.5**)- Material: The focus is on sections 2.1-2.3, 2.5-2.6, 3.1-3.2, and the notes on coordinates. (Of course, math is very cumulative, so concepts from Chapter 1 may reappear!)
- One practice midterm and solutions.
- A second practice midterm and solutions. (Problem 5 is phrased in a way we haven't talked about, but you can do it by moving the entries of a 2x2 matrix to a 4x1 vector).
- A third practice midterm and solutions. (Problems 5 and 6 aren't things we cover).
- Suggested problems for Section 3.1 (Introduction to determinants): 9, 11, 13, 15-18, 19, 21
- Suggested problems for Section 3.2 (Properties of determinants): 1-4, 4, 7, 9, 15-20, 21, 25, 29

- Quiz 7 - Tuesday March 14 (Solution)
- Material: Section 4.1 from the textbook.
- Suggested problems for Section 4.1 (Eigenvectors and eigenvalues): 1-8, 9, 11, 13, 15, 17-20

- Quiz 8 - Tuesday March 21 (Solution)
- Material: Sections 4.2 and 4.3 from the textbook.
- Suggested problems for Section 4.2 (The Characteristic Equation): 1, 3, 5, 7, 9, 11, 13, 15, 17, 18
- Suggested problems for Section 4.3 (Diagonalization): 1, 3, 5, 7, 9, 11, 15, 17, 23, 24, 27

- Quiz 9 - Tuesday March 28 (Solution)
- Material: Sections 4.4 and 4.6 from the textbook.
- Suggested problems for Section 4.4 (Eigenvectors and Linear Transformations): 11-18, 21, 22, 29
- Suggested problems for Section 4.6 (Discrete Dynamical Systems): 1, 3-7, 15
- The additional dynamical systems notes also have exercises and solutions (we cover section 1 only).

- Quiz 10 - Tuesday April 4 (Solution)
- Material: Sections 5.1, 5.2, and 5.3 from the textbook (material from 5.3 depends on how much gets covered in class on March 30).
- Suggested problems for Section 5.1 (Inner Product, Length, Orthogonality): 1, 3, 5, 7, 9, 11, 13, 15, 17, 24, 31
- Suggested problems for Section 5.2 (Orthogonal Sets): 1, 3, 5, 7, 9, 13, 17
- Suggested problems for Section 5.3 (Orthogonal Projections): 1, 3, 5, 11, 13, 15

**Final exam - Tuesday April 25 at 12:00, in SRC A-B-C**- Material: Everything from the whole semester!
- The practice problems listed above for the semester are generally still a good representative of what you should be able to do. If you've done them already and want more, similar ones in the text (many of the even-numbered ones for instance) that aren't on my list are good practice.
- Suggested problems for Section 5.5 (Least-Squares Problems):
1, 3, 5, 7, 9, 11, 13, 19, 21. Also problems 1 and
3 in Section 5.6 could be relevant. (Note we
*do not*cover the QR factorization problems in 5.5.). - Resources for old final exams:
- Many past finals are available on the department website.
- There is a UBC wiki with discussion of solutions to some past exams.
- The UBC math club sells packs of past exams and solutions.

There are additional practice problems available on WebWork.