All exercises are taken from the textbook. The list may be adjusted as the term progresses. New questions will be in red, and deleted questions will be stroked out.
If we don't cover a section completely, the comments column below will indicate this, but this may also change as the term progresses.
If a question number is a hyperlink, then clicking on the link will provide more information about the question. (Currently 1.4 Q35 and 2.2 Q31.)
In order to become familiar with the material, you will probably have to solve more exercises than the ones given below. (Recall that the questions in quizzes and exams will not simply be these exercises with changed numbers!)
| Section | Exercises | Comments |
|---|---|---|
| Section 1.1 | 1, 3, 5, 7, 9, 11, 13, 17, 21, 29, 33, 43, 55 | The dot product is defined in Section 1.2. |
| Section 1.2 | 3, 9, 15, 17, 25, 33, 41, 47, 49, 66 | |
| Section 1.3 | 1, 3, 5, 7, 9, 11, 13, 15, 19, 21, 23, 27, 29 | |
| Cross products | 1, 2, 4, 8(c) | Know the properties listed in Ex. 5 (but not Ex. 6) |
| Section 1.4 | 15, 17, 19, 21, 23, 27, 31, 35 (click for solution) | Only code vectors |
| Section 2.1 | 1, 3, 9, 11, 13, 15, 17, 21, 23, 29, 31, 37 | |
| Section 2.2 | 5, 7, 9, 11, 15, 21, 23, 29, 31, 33, 35, 37, 45, 47, 49 | No systems over Zp |
| Section 2.3 | 1, 5, 9, 15, 19, 23, 25, 27, 29, 33, 35, 37 | |
| Section 2.4 | 15, 17, 19, 21 | Network analysis and electrical networks |
| Section 3.1 | 1, 7, 9, 13, 15, 17, 21, 31, 35, 38(a), 39 | |
| Section 3.2 | 3, 5, 7, 13, 27 | |
| Section 3.3 | 1, 3, 9, 11, 13, 15, 23, 53, 55, 57 | No elementary matrices or inverses over Zm |
| Section 3.5 | 3, 7, 11, 15, 19, 23, 29, 31, 37, 39, 41, 45, 51 | |
| Section 3.6 | 1, 3, 7, 11, 17, 20, 21, 31, 37, 40 (look at 38(a) in Sec. 3.1 if you're stuck) | |
| Section 3.7 | 5-9 | Only Markov chains |
| Section 4.1 | 5, 7, 11, 13, 21, 23, 27, 29, 37 | |
| Section 4.2 | 5, 9, 13, 23, 27, 29, 31, 33, 39, 45, 49, 51, 53, 57, 59, 61 | |
| Section 4.3 | 1, 3, 5, 7, 9, 11, 15, 19, 23 | |
| Section 4.4 | 1, 3, 7, 9-15, 19, 21, 25, 37 | |
| Section 4.6 | 7 and also see below | Only Markov chains? |
| Section 5.1 | 3, 5, 7, 9, 13, 15, 17, 19, 21, 29, 31 | Only check for rotations in Ex. 29 and 31 |
| Section 5.2 | 1, 3, 5, 7, 9, 11, 13, 17, 21 | |
| Section 5.3 | 1, 3, 5, 7, 9, 11, 13, 15 | |
| Section 5.4 | 3, 5, 9, 13, 17, 21 | |
| Section 5.5 | Not covered. | |
| Appendix C | 3, 5, 9, 17, 21, 23, 33, 35 | Numbers refer to the "Appendix Exercises" (copy here; solutions). |
Exercise for Section 4.6:
Take the matrix from Exercise 7 in that section.
a) Find the equilibrium state y for a total initial population of 10.
b) Show that in the long run any initial state x0=[a,b] with a+b=10
tends to the equilibrium state y found in (a).
Solution.
Here are four practice midterms: MT1 Winter 2013, MT2 Winter 2013, MT1 Fall 2013, MT2 Fall 2013. Here are the same four exams, with solutions: MT1 Winter 2013, MT2 Winter 2013, MT1 Fall 2013, MT2 Fall 2013. Try the problems first without looking at the solutions!
No practice final exams are available.
Solutions to quizzes for two different sections are available here. Even if these are not from your section, you may find them useful for studying.