### Homework (Recommended Problems)

These exercises are not to be handed in for marking. Instead, you are encouraged to work on these selected exercises as part of your studying for the course.

- Here are the recommended homework problems for the
- 4th edition
- 3rd edition (use the 3rd edition if you are using the exercise set on D2L)

### Textbook Corrections

- Section 4.1: for Question 27, if you are wondering why your answer of [-
i , 1] is different than the book's answer, remember that any multiple of an eigenvector is also an eigenvector for that lambda. So multiply your vector byi and you'll get the book's answer. - Section 4.2:
- the answer to Question 7 has a typo: the first entry in the null space should be -1, not +1.
- for Question 9, if you got [5, -1, 7, 0] and [-3, 2, 0, 7] as your column vectors, then that's a fine answer. The book's anwer is also correct: since [1, 0, 2, 1] = 2/7 [5, -1, 7, 0] + 1/7 [-3, 2, 0, 7], so the book's vectors are in the same plane as my answer, but it's not obvious to me why they chose those vectors rather than the more straightforward ones that we get with the standard procedure.

- Section 5.4: if you are wondering why the second column in the matrix Q has the bottom entry negative rather than the top, what they have is also an eigenvector for lambda=3, it's just been multiplied by -1. So if your answer is the same except the textbook's except that your top entry for the second column is the one that's negative, your answer is perfectly fine.

### Practice Questions

- Gilles' Practice Problems, including answers
- For Test #1, do questions 1 to 6, 8 (question 7 is from Section 2.4)
- For Test #2, do questions 7, 9 to 20
- For Test #3, do questions 21 to 28, 29(a)
- Susie has full solutions to these problems on her Math 251 website – look for the links in the table at the bottom of the page.

- Leah's Practice Problems, with Solutions Part I, Solutions Part II, and Solutions Part III
- For Test #1, do questions 1 to 6
- For Test #2, do questions 7, 8, 10 to 14
- For Test #3, do questions 16, 17, 18, 20, 23, 24, 26, 29