return to Fall 2025 MATH 5333 webpage
| Required (free) textbook: | Linear Algebra Done Right, 4th Ed, by S. Axler, UTM, Springer. A list of known errata for this book is posted here. Videos by the author to accompany the book can be found here. |
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- Homework will not be collected.
- There might be more than one correct answer for any given question.
- Dates indicate homework assigned in lecture on that date. Dates for future assignments are tentative and subject to change.
- If you notice some questions are in a nonincreasing order, then it means that the order is recommended by your instructor and is usually chosen to match the order in which the material was presented in class.
- Any question of the form Hi (i = 1,….) is designed to help you answer some textbook questions – make sure you answer any Hi question before working on a textbook problem that is listed after it.
- Any optional exercises are for those students who wish to explore some of the ideas in more depth – those questions are NOT game for the tests.
- Skimming through the main ideas in a section shortly before that section is covered in class should help you understand the lecture – try it!
- If any of the mathematics below does not display properly (e.g., an error message received), compare with this file from 2022.
- Any UTA students who are vision impaired and need help reading the mathematics on this webpage should consult with UTA’s SARC for assistance.
- The homework from Fall 2022 can be viewed here; in particular, it will give you a rough outline of what material will be presented and how many lectures will be spent on each item. However, that homework was assigned from the previous edition of the textbook.
- Recall that our test dates are: Sept 11, Oct 9, Nov 6 and Dec 9.
- LAST REVISION: 9/23/25.
| Aug 19 | Check your Canvas notifications to check you can receive Canvas announcements. Attendance will be noted, starting today. Read course syllabus carefully. Make a note of the test dates in your calendar. Review course website and repeat frequently during the semester. Review the course’s Canvas portal. Read this list of study techniques and read https://www.jeffreybennett.com/pdf/How_to_Succeed_general.pdf for ideas on how to study most effectively. Read your lecture notes (meaning the notes you should have taken during lecture) and pgs 1-10, 12-16. Do 1A: 1, 7, 9 10 13 & 1B: 4. Read pgs 119-120. |
| Aug 21 | Read your lecture notes & pgs 18-24. Do 1B: 6, 8, 1, 2 & 1C: 1, 3-6, 10, 12, 15, 14. Do the following questions on past UTA preliminary examinations (see Canvas for how to access them): Jan 2013 #3(a), Jan 2014 #3, Jan 2015 #2(b). Read pg 121. |
| Aug 26 | Read your lecture notes & pgs 27-36. Do 1C: 20, 21, 23 & 2A: 2-8, 11, 13. Read pgs 122-123 and these notes about writing proofs. By this time, you have seen quite a few theorems. It is best NOT to memorize the theorems, but to do enough of the homework that the results of the theorems become known to you, though perhaps with different wording or using pictures. |
| Aug 28 | Read your lecture notes & pgs 39-42, 44-48. Do 2A: 15-18 & 2B: 3, 4, 6, 7. Read pgs 123-124. |
| Sep 02 | Read your lecture notes & pgs 44-48. Do 2C: 1-5, 7, 10-14 and the following questions on past UTA preliminary examinations: Jan 2013 #3(b)-(d), Aug 2014 #2(a), Jan 2015 #2(c)(d). Read pgs 124-125. |
| Sep 04 | Read your lecture notes & pgs 52-56. Do 3A: 1, 3, 4, 7, 12, 13, 16. Read pg 126. Test 1 will be 1 week from today; check Canvas for an information sheet. |
| Sep 09 | Read your lecture notes & pgs 59-65. Do 3B: 1, 2, 6, 9, 10, 12-14, 27, 30. Read pg 127. Test 1 will be on Thursday; check Canvas for an information sheet. |
| Sep 11 | Read your lecture notes & pgs 69-73. Do 3C: 4 and the following questions on past UTA preliminary examinations: Jan 2013 #1(a), Jan 2025 #3(a)(b), Aug 2025 #3(b)(i)(ii). Read pgs 127-128. Test 1 is today; check Canvas for an information sheet. |
| Sep 16 | Read your lecture notes & pgs 69-73. Do 3C: 6, 7, 14. Read pgs 128-129. Look over the solutions to Test 1 on Canvas; use password “math5333” to open the file. Read through the suggestions of study techniques from Aug 19 above and see which one(s) might work for you. |
| Sep 18 | Read your lecture notes & pgs 76-79 & pgs 82-84. Do 3C: 17 and 3D: 1, 4, 9, 10 (hint: use FTLM as suggested by book’s hint or consider matrices). |
| Sep 23 | Read your lecture notes & pgs 84-93. Do 3D: 20, 21, 23, 24. |
| Sep 25 | Read your lecture notes & pgs 105-107. Do 3F: 1, 3, 4, H1, 9, 10 (hint: use #9), 11, where H1 is H1: Suppose, without proof, that B = Find the dual basis of the dual space ( ℝ3 )′ relative to B. |
| Sep 30 | Read your lecture notes & pgs 107-113. Do 3F: 13-15, 22 (hint: consider dimension for (b)). |
| Oct 02 | Read your lecture notes & pgs 135-139. [Optional: read pgs 132-134.] Do 5A: 1, 8-10, 13, 19-21, 25, 26 (hint: use #25). Do the following question on past UTA preliminary examinations: Aug 2013 #3(b)(ii). Test 2 will be 1 week from today; check Canvas for an information sheet. |
| Oct 07 | Read your lecture notes & pgs 143-145 & pgs 148-150. Do 5B: 1, 3, 11, 12, 14, 20, 22-24. Test 2 will be on Thursday; check Canvas for an information sheet. |
| Oct 09 | Test 2 is today; check Canvas for an information sheet. |
| This row and the subsequent empty rows will be filled as the semester progresses. | |
The above empty rows will be filled as the semester progresses. The assignments from Fall 2022 can be viewed in their entirety here . However, note that Fall 2022’s homework was assigned using the previous edition of the textbook, so the page numbers and question numbers might not match. Nevertheless, Fall 2022’s homework will give you a rough idea of how many lectures will be assigned to each topic, which topics will be covered, and roughly the amount of homework to be assigned per topic. |