For Monday, 11 December: Read §5.5 (6e: pp. 304–309; 5e: pp. 297–302). Suggested exercises (not required): 1, 7, 13, 23–28 (6e) or 1, 7, 13, 23, 24 (5e). You can submit your work on Canvas for extra credit. If you didn't complete the worksheet on Friday, you can submit it on Monday instead. Let me know what you would like to review during the last week of class.
For Friday, 8 December: Read §5.4 (6e: pp. 297–302; 5e: pp. 290–295). Do the practice problems (6e: p. 302; 5e: p. 295) and check your answers (6e: p. 304; 5e: p. 297). Do the worksheet. Do exercises 33, 34 from §5.3 and exercises 1, 4, 5, 9, 13, 17, 18, 20 (6e) or exercises 27 and 28 from §5.3 and exercises 1, 3, 5, 8, 9, 11, 13, 17, 27 from §5.4 (5e). Submit your work on Canvas. Complete the homework self-assessment.
For Wednesday, 6 December: Read §5.3 (6e: pp. 290–295; 5e: pp. 283–288). Do the practice problems (6e: p. 295; 5e: p. 288) and check your answers (6e: pp. 296–297; 5e: p. 290). Do exercises 4, 5, 7, 11, 19, 21–30, 37, 38 (6e) or 4, 5, 7, 11, 19, 21, 22, 31, 32 (5e) from §5.3. Submit your work on Canvas. Complete the homework self-assessment.
For Monday, 4 December: Read §5.2 (6e: pp. 282–288; 5e: 276–281). Do the practice problem (6e: p. 288; 5e: p. 281) and check your answer (6e: p. 289; 5e: p. 283). Do exercises 40–43 from §5.1 and exercises 1, 5, 9, 17–30 from §5.2 (6e) or do exercises 32–35 from §5.1 and exercises 1, 5, 9, 17–22 from §5.2 (5e). Submit your work on Canvas. Complete the homework self-assessment.
For Friday, 1 December: Read §5.1 (6e: pp. 274–279; 5e: pp. 268–273). Do the practice problems (6e: p. 279; 5e: p. 273) and check your answers (6e: p. 282; 5e: pp. 275–276). Do problems 1–5, 9, 15, 19, 21–32, 34–40 (6e) or 1–5, 9, 15, 19, 21–24, 26–32 (5e). Submit your answers on Canvas. Complete the homework self-assessment.
For Wednesday, 29 November: Read the section on change of basis (6e: §4.6, pp. 249–253; 5e: §4.7, pp. 241–244). Do the practice problems (6e: p. 253; 5e: p. 244) and check your answers (6e: p.255; 5e: 246). Do exercises §4.5, #54 and §4.6, #1, 3, 5, 7, 11–15, 19, 20 (6e) or §4.5, #34 and §4.7, #1, 3, 4, 7, 11–13, 17, 18 (5e). Submit your work on Canvas. Complete the homework self-assessment.
For Monday, 27 November: Review chapter 4 (6e: §§4.1–5; 5e: §§4.1–4.6). Do the practice problems and submit your work on Canvas. Feel free to use ChatGPT to help, but make sure you understand what it is telling you: in my tests, ChatGPT 4 got more than half of the problems wrong; it also chose unnecessarily complicated approaches for some of the problems it got right. Complete the homework self-assessment.
For Friday, 17 November: Do exercises 41, 43–49, 51, 52 (6e: pp. 247–249) or 27, 29–32 (5e: pp. 231–232) from §4.5. Submit your work on Canvas. Complete the homework self-assessment.
For Wednesday, 15 November: Do exercises 25–30 (6e: p. 239) or 21–26 (5e: p. 225) from §4.4. Read §4.5 (6e: pp. 241–247; 5e: pp. 227–230). Do exercises 3, 7, 11, 17–27, 29, 33, 35, 37, 39 (6e: pp. 247–249) or 3, 7, 13, 19–21, 23, 27, 29, 31, 33 (5e: pp. 231–232) from §4.5. Submit your work on Canvas. Complete the homework self-assessment.
For Monday, 13 November: Read §4.4 (6e: pp. 231–238; 5e: pp. 218–224) and do the practice problems (6e: p. 238; 5e: p. 224) and check your answers (6e: p. 240; 5e: pp. 226–227). Do exercises 1, 3, 5, 7, 13, 15–22, 24, 31, 33 (6e: pp. 224–226) or 1, 3, 5, 7, 13, 15–18, 20, 27, 29 from §4.4. Submit your work on Canvas. Complete the homework self-assessment.
For Friday, 10 November: Read §4.3 (6e: pp. 222–228; 5e: pp. 210–215) and do the practice problems (6e: p. 228; 5e: 215). Do exercises 1, 3, 7, 9, 15, 19, 21–35, 37, 41, 43, 44 (6e) or 1, 3, 7, 9, 15, 19, 21–23, 25, 29, 31, 32. Submit your work on Canvas. Complete the homework self-assessment.
For Wednesday, 8 November: Read §4.2 (6e: pp 211–219; 5e: pp. 200–207) and do the practice problems (6e: p. 219; 5e: p. 207). Finish watching 3blue1brown's introduction to vector spaces. Do exercises 1, 5, 7, 11, 15, 25–38, 43, 45, 48 (6e) or 1, 5, 7, 11, 15, 25, 26, 31, 33, 36 (5e). Submit your work on Canvas. Complete the homework self-assessment.
For Friday, 3 November: Read §4.1 (6e: pp. 202–208; 5e: pp. 192–197) and do the practice problems (6e: p.208; 5e: 197). Watch 3blue1brown's introduction to vector spaces (for Friday, we will only need to understand the first 4 minutes and last 5 minutes of this video). Do exercises 1, 3, 5–8, 11, 15, 19, 21, 23–32, 40, 41 (6e) or 1, 3, 5–8, 11, 15, 19, 21, 23, 24, 31, 32. Submit your work on Canvas. Complete the homework self-assessment.
For Wednesday, 1 November: There will be a make-up exam. This exam will replace the lower of your scores on the first two exams. If you are satisfied with your scores on those exams, you are not required to take the exam.
For Monday, 30 October: There is no assignment. Let me know if you have questions for the last day of review.
For Friday, 27 October: We will review §§3.1–3. Please reread these sections. Do exercises 9, 11, 15, 30, 34 (6e) or 9, 11, 15, 22, 26 (5e) from §2.9; do exercise 37 (6e or 5e) from §3.1; do exercises 23, 24, 38, 45 (6e) or 23, 24, 32, 39 (5e) from §3.2. Submit your work on Canvas. Complete the homework self-assessment.
For Wednesday, 25 October: We will review §§2.8–9. Please reread these sections. Do exercises 23–32, 34, 35, 37, 38 (6e) or 15–24, 26, 27, 29, 30 (5e) from §2.3 and exercises 6, 17, 20 (6e or 5e) from §2.8. Submit your work on Canvas. Complete the homework self-assessment.
For Monday, 23 October: We will review §§2.1–3. Please reread these sections. Do exercises 27, 31–34 (6e) or 19, 23–26 (5e) from §2.1, exercises 22, 24, 26, 31–34, 47, 48 (6e) or 12, 14, 16, 21–24, 37, 38 (5e) from §2.2. Sumbit your work on Canvas. Complete the homework self-assessment. If you scored 3.5/4 ( = 87.5% ) or higher on Exam 2, you are not required to complete this assignment and you are not required to attend class.
For Wednesday, 18 October: The second exam is in class on Wednesday! There is no assignment other than to prepare for it. The exam will focus on Chapters 2 and 3 of the book (but Chapter 1 will be tested implicitly since it is used in Chapters 2 and 3). You may find this summary of the invertible matrix theorem helpful. All of our in-class worksheets are on Canvas and may be useful in your studying. To assist with your preparation, you can find all of the worksheets from previous classes on Canvas.
For Monday, 16 October: Read §3.3 (6e: pp. 188–195; 5e: pp. 179–186), do the practice problem (6e: p. 195; 5e: p. 186), and check your answer (6e: p. 197; 5e: p. 187). Watch 3blue1brown's video on determinants. Do exercises 5, 7, 11, 19, 25, 30, 35–38 (6e) or 5, 7, 11, 19, 25, 30 (5e). Submit your work on Canvas. Complete the homework self-assessment.
For Friday, 13 October: Read §3.2 (6e: pp. 179–185; 5e: 171–176), do the practice problems (6e: p. 185; 5e: pp. 176–177), and check your answers (6e: p. 187; 5e: p. 179). Do exercises 5, 9, 11, 15, 17, 19, 21, 25, 27–34, 37–42 (6e) or 5, 9, 11, 15, 17, 19, 21, 25, 27, 28, 31–36 (5e). Watch Khan's calculation of a determinant by row operations. One of your classmates found this video helpful for understanding problem 43 from §3.1 (and got an extra credit point for suggesting it). Submit your work on Canvas. Complete the homework self-assessment.
For Wednesday, 11 October: Read §3.1 (6e: pp. 172–176; 5e: 166–169), do the practice problem (6e: p. 176; 5e: 169), and check your answer (6e: p. 179; 5e: 171). Watch Khan's introduction of determinants. Khan also has a video on 3 × 3 determinants that you may find useful. Do exercises 1, 3, 13, 19, 21, 24, 37, 39–43 (6e) or 1, 3, 13, 19, 21, 24, 37, 39–41 (5e). Submit your work on Canvas. Complete the homework self-assessment.
For Monday, 9 October: There is no new reading assignment for Monday. We will continue work on §2.9 in class, so you may wish to review §2.9. Do exercises 1–15, 17, 18, 22, 26, 30–32 (6e) or 1, 3, 4, 8, 12, 16–18 (5e) from the supplementary exercises for chapter 2 (6e: pp. 169–170; 5e: pp. 162–163). Submit your work on Canvas. Complete the homework self-assessment.
For Friday, 6 October: Read §2.9 (6e: pp. 162–166; 5e: 155–159). Do the practice problems on p. 166 (6e) or p. 159 (5e) and check your answers on pp. 168–169 (6e) or pp. 161–162 (5e). Optional videos: 3blue1brown's video on basis vectors, Khan's video on bases, and Strang's video on bases. Do exercises 1, 5, 11, 13, 17–26, 29, 33. Submit your work on Canvas. Complete the homework self-assessment.
For Wednesday, 4 October: Read §2.8 (6e: pp. 155–159; 5e: 148–152). Do the practice problems on p. 159 (6e) or p. 152 (5e) and check your answers on p. 162 (6e) or p. 155 (5e). Watch Khan's video on subspaces. Do exercises 1–4, 7bc, 9, 15, 17, 19, 21–30, 33. Submit your work on Canvas. Complete the homework self-assessment.
For Monday, 2 October: Read §§2.6–2.7 (6e: pp. 141–145, 147–153; 5e: pp. 134–137, 140–146). Do the practice problems on p. 145 and p. 153 (6e) or p. 138 and p. 146 (5e) and check your answer on p. 147 and p. 155 (6e) or p. 140 and p. 148 (5e). Do exercises 5, 7, 11 12 from §2.6 and 2, 3, 7, 15 from §2.7 (same numbering in both editions). Watch this video from 3blue1brown. Submit your work on Canvas. Complete the homework self-assessment.
For Friday, 29 September: Read §2.5 (6e: pp. 132–138; 5e: pp. 125–131). Do the practice problem on p. 138 (6e) p. 131 (5e) and check your answer on pp. 140–141. Watch these twovideos on LU factorization by Gilbert Strang and Ben Harris and watch this video about problem #2 from Wednesday's worksheet. Do exercises 1, 9, 17, 19, 21, 26 (this is an idea we will see again later) on pp. 138–140 (6e) or pp. 131–133 (5e) from §2.5. Submit your work on Canvas. Complete the homework self-assessment.
For Wednesday, 27 September: Read §§2.3–2.4 (6e: pp. 121–123, 126–130; 5e: pp. 113–116, 119–123). Do the practice problems on pp. 123, 130 (6e) or pp. 118–116, 123 (5e) and check your answers on pp. 126, 132 (6e) or pp. 119, 125. Watch these twovideos from Khan Academy about invertibility. Do exercises 3, 5, 11–22, 23, 25, 29, 32, 35, 45 from §2.3 on pp. 124–125 and 15–17, 27 from §2.4 on pp. 130&dnash;132 (6e) or 3, 5, 11–12, 15, 17, 21, 24, 27, 37 from §2.3 on pp. 117–118 and 13–15, 25 from §2.4 on pp. 123–125 (5e). Submit your work on Canvas. Do the homework self-assessment.
For Monday, 25 September: Read §2.2 (6e: pp. 111–118; 5e: pp. 104–111). Do the practice problems on p. 118 (6e) or p. 111 (5e) and check them on p. 120 (6e) or 113 (5e). Watch Khan Academy's example of finding a matrix inverse. Watch this MIT video on matrix inversion. At around 1:20, Pires lists some situations where matrices are not invertible; can you figure out why a repeated row or column, or a row or column of zeroes means that a matrix is not inverible?. Do problems 1, 7, 9, 11–20, 22, 23, 25, 29, 33, 41, 43, 47 (6e) or 1, 7, 9, 10, 12, 13, 15, 19, 23, 31, 33, 37 (5e). On problem 47 (6e) or 37 (5e), can you use the method we worked on in class today? Submit your homework on Canvas. Complete the homework self-assessement.
For Friday, 22 September: Read §2.1 (6e: pp. 98–108; 5e: pp. 94–102). Do the practice problems on p. 108 (6e) or p. 102 (5e) and check your answers on pp. 110–111 (6e) or p. 104 (5e). Watch 3blue1brown's video on matrix multiplication. Watch Khan Academy's video on composition of linear transformations. Do §2.1, exercises 1, 3, 5, 7, 9, 15–24, 27, 31, 33, 35, 47 (6e) or 1, 3, 5, 7, 9, 15–16, 19, 23, 25, 27, 39 (5e). Submit your work on Canvas (your grade will be based on completion). Complete the homework self-assessment.
For Wednesday, 20 September: The first exam is in class on Wednesday!. There is no assignment other than to prepare for it. To assist with your preparation, you can find all of the worksheets from previous classes on Canvas.
For Monday, 18 September: Read §1.9 (6e: pp. 75–82; 5e: pp. 71–78). Do the practice problems on p. 82 (6e) or p. 77 (5e) and check your answers on p. 84 (6e) or pp. 80–81 (5e). Watch this video by 3blue1brown and this video from Khan Academy. Do problems 1, 3, 7, 13, 15, 23–32, 45, 47 (6e) or 1, 3, 7, 13, 15, 23–24, 37, 39 (5e) from §1.9. Remember, answers to the odd-numbered questions can be found in the back of the book. Complete the homework self-assessment.
For Friday, 15 September: Read §1.8 (6e: pp. 67–71; 5e: pp. 63–69). This section is the most abstract so far, so it may be worth devoting some extra attention to it. Watch 3blue1brown's video on linear transformations. Watch Khan Academy's video on linear transformations. Khan also has an interactive introduction to linear transformations. Do the practice problems on p. 71 (6e) or p. 69 (5e) and check your answers on p. 74 (6e) or p. 71 (5e). Do exercises 1, 5, 7, 9, 11, 17, 21–26, 28–29, 37, 39, 41 on pp. 72–74 (6e) or 1, 5, 7, 9, 11, 17, 21, 22a–d, 29, 31, 33 on pp. 69–71 (5e) from §1.8. Complete the homework self assessment.
For Wednesday, 13 September: Read §1.7 (6e: pp. 60–64; 5e: pp. 56–60). When reading, create your own examples of lists of vectors and test whether they are linearly independent according to the definition. Watch the rest of 3blue1brown's video on linear independence and span. Watch Khan Academy's video on linear independence. (Khan has a second video that you may find useful.) Do the practice problems on p. 64 (6e) or p. 61 (5e) and check your answers on p. 66 (6e) or p. 63 (5e). Do exercises 1, 3, 5, 9, 15, 17, 19, 21–28. Complete the homework self assessment.
For Monday, 11 September: Read §1.5 (6e: pp. 46–50; 5e: pp. 43–47). Watch this video by Martina Balagovic (please note that she uses the term "special solution" where the textbook would say "solution to the homogeneous system"). For a more extended discussion, you may also want to look at the first halves of these twovideos (after 25 minutes, both videos get into some topics we haven't gotten to yet). Do the practice problems on p. 51 (6e) or p. 47 (5e). Do exercises 1, 5, 11, 21, 27–28, 30–36, 41–44 (6e) or 1, 5, 11, 17, 23acde, 24, 29–32 (5e). Do the homework self assessment.
For Friday, 8 September: Read §1.4 (6e: pp. 37–41; 5e: pp. 35–40). Watch this video from Khan Academy. Do the practice problems on p. 41 (6e) or p. 40 (5e) and check your answers on p. 44 (6e) or pp. 42–43 (5e). Do exercises 1–5, 9, 13, 24–34, 41, 43, 47 (6e) or 1–5, 9, 23b–f, 24, 31, 33, 37 (5e). Complete the homework self assessment.
For Wednesday, 6 September: Read §1.3 (6e: pp. 26–33; 5e: 24–31). Watch these twovideos by 3blue1brown. Do the practice problems (6e: p. 33; 5e: p. 32) and check your answers (6e: p. 36; 5e: p. 40). Fifth edition: from §1.3, do exercises 1, 3, 5, 7, 9, 11, 17, 23, 24, 29, 32. Sixth edition: from §1.3, do exercises 1, 3, 5, 7, 9, 11, 17, 23–33, 37, 40. (You do not need to submit any work.) Complete the homework self assessment.
For Friday, 1 September: If you haven't already done so, complete the classwork self-assessment. Read §1.2 (pp. 13–23). Watch Khan Academy's video on Gaussian elimination. (Khan has a second video that you may also find useful.) Do the practice problems at the end of §1.2 (p. 23) and check your answers (p. 25). Do the following exercises from §1.2: 1, 3, 5, 7, 19, 21, 25–34 in the 6th edition (1, 3, 5, 7, 15, 17, 21–22 in the 5th edition). Complete the homework self assessment.
For Wednesday, 30 August: Read §1.1 (pp. 3–9). Watch this video on Gaussian elimination. Do the practice problems at the end of §1.1 (p. 9) and check your answers (p. 12). Do problems 3, 5, 14, 18, 23, 27–32, 34, 39–42 (do not submit these). (5th edition problems: 3, 5, 14, 18, 23, 24, 29–32.) In case you do not yet have the textbook, here is a scan of the first chapter (CU login required). After completing this homework, but before class, complete a self assessment about the homework (this is not anonymous, but it will not affect your grade).