Math 24
Linear Algebra
Last updated March 10, 2021 12:04:08 EST

General Information HW Assignments Canvas Page Lecture Videos


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Homework Assigments


Week of January 4 to January 8
Assignments Made on:
Monday:
  • Study:
  • Do:
Wednesday:
  • Study:
  • Do:
Friday:
  • Practice Exam and Survey: I have created a survery in the form of a practice exam on gradescope. You should login to gradescope, download "m24-exam-survey" and complete it (you'll have two hours). Then scan, upload, and link your responses. Please do this by Monday evening.
  • Study: Read sections 1.1 and 1.2 of the text.
  • Do:
    1. Show that in an ordered field $\mathbf F$, we always have $1>0$. (Start by showing that $(-1)^2=1$.) Conclude that if $x<0$ and $y<0$, then $xy>0$.
    2. Is it possible to make the complex numbers $\mathbf C$ into an ordered field?
    3. If $V$ is a vector space over $\mathbf F$ and $ax=\mathbf 0$, for some $a\in \mathbf F$ and $x\in V$, then either $a=0$ or $x=\mathbf 0$. (Here $0$ denotes the zero element of the field $\mathbf F$ and $\mathbf 0$ is the zero vector in $V$. I suggest using Theorem 1.2 from the text.)


Week of January 11 to January 15
Assignments Made on:
Monday:
  • Study: Read section 1.2 and start section 1.3. Having a look at Appendices A and B would be helpful. Also Appendic C on fields might help with the first lecture and the first homework assignment. But now we are going to settle down and concentrate on the fields like the rationals, the reals, or later the complex numbers.
  • Do: In Section 1.2: 16, 18, and 21
  • First Homework Due: Friday's assignment and today's asignment will be due via gradescope by 10am Wednesday.
Wednesday:
  • Study: Read section 1.3.
  • Do: In Section 1.3: 3, 19, 23, 28 (Hint: consider #5), and 30.
Friday:
  • Study: Read Section 1.4. Note that there is no class on Monday (January 18th). Wednesday and today's assignment is due via gradesscope on Wednesday by 10am.
  • Do: In Section 1.4: 6 (assume $\mathbf F$ does not have characteristic $2$ here), 14, and 15. You should not turn in problems 7, 8, and 9, but you should be aware of the results (and that they are straightforward to prove).


Week of January 18 to 22
Assignments Made on:
Monday:
  • Study: No Class: MLK Holiday
  • Do:
Wednesday:
  • Homework Solutions: Here are selected solutions for the homework. (Last modified January 18, 2021)
  • Study: Read Section 1.5.
  • Do: 8 ($\mathbf F$ having characteristic $2$ just means $1+1=0$), 9, and 19.
Thursday (x-hour):
  • Study: Start Section 1.6
  • Do: In Section 1.6: 3b and 11.
Friday:
  • Study: Finish Section 1.6 and Start Section 2.1. Note that we are not covering Section 1.7 and you are not responsible for it. Please pay particular attention to Examples 2, 3, and 4 in section 1.6 as they will not be covered in lecture.
  • Do:
    • In Section 1.6: 14, 17, and 23.
    • In Section 2.1: 9abc and 11. (Have a look at 1, but do NOT turn it in.)


Week of January 25 to January 29
Assignments Made on:
Monday:
  • Study: Finish Section 2.1 and start Section 2.2. There is a lot of material in these sections and we won't be able to cover it all in lecture. So a careful reading is advised.
  • Do:
    • In Section 1.6: 33a.
    • In Section 2.1: 17 and 27ab. (I also suggest looking at, but not turning in, 1, 10, and 12.)
    • In Section 2.2: 4, 8, and 10. (Also problem 5 would be good practice. The answers in the back of the text.)
  • Third Homework: The assignments from Wednesday, Thursday, and Friday last week, as well as todays assignment is due Wednesday via gradescope.
Wednesday:
  • Study: Finish Section 2.2 and start Section 2.3.
  • Do: In Section 2.2: 14 and 17 (these are problems 13 and 16 in the 4th edition). (For 17, consider the proof of the Dimension Theorem.)
Friday:
  • Study: Finish Section 2.3 and start Section 2.4.
  • Do:
    • In Section 2.3: 11, 12, and 13.
    • In Section 2.4: 4 and 6.


Week of February 1 to 5, 2021
Assignments Made on:
Monday:
  • Study: Finish Sections 2.4 and 2.5.
  • Do:
    • In Section 2.4: 15.
    • In Section 2.5: 7a and 10a (in the 4th edition it is just problem 10). You should work, but don't turn in, 4 and 5 (the answers are in the back of the text). You might want to think about 10b.
Wednesday:
  • Study: We are skipping Sections 2.6 and 2.7. Read Section 3.1 and start Section 3.2.
  • Do: No written assignment today. But you are always well advised to look carefully at quesiton 1 in Section 3.1 (and in every section we finish). Especailly have a look at problem 3 (the answers are in the back of the text). Try to work problem 12 using induction, but don't turn it in.
Friday:
  • Study: Finish Section 3.2. There is a lot in this section. Careful reading and review of the lecture would be wise. There is a lot of computational work in this section as well as theory. Be sure to work a selction of the parts of 1, 2, 4, 5, and 6 where answers are provided in the back of the text.
  • Do: In Section 3.2: 8, 14, 17, and 21. For 21, notice that if $\operatorname{rank}(A)=m$, then $L_A$ is onto.


Week of February 8 to February 12
Assignments Made on:
Monday:
  • Study:Read Section 3.3. We may not finish all of Section 3.3 today. We are not covering the Leontief model at the end of the section.
  • Do: In Section 3.3: 5 and 8. You don't have to turn them in, but it would wise to look at question 1, 2, 3, and 4 where the answers are in back of the text.
Wednesday:
  • Study: Read Section 3.4.
  • Do: In Section 3.4: 3 and 10. For 10, see Example 4 in the text. Do not turn in, but you should look at the parts of 1, 2, and 4 that have answers in the back of the text.
Friday:
  • Study: Skim Section 4.1. We are not covering the material on the area of a paralleogram. Read Section 4.2 through Theorem 4.4.
  • Do:
    • In Section 4.1: 5 and 7. You should also work, but not turn in, 2 and 3a.
    • In Section 4.2: 6, 12, 23, and 26. (Problem 23 requires Theorem 4.4.)


Week of Februrary 15 to 19
Assignments Made on:
Monday:
  • Study: Finish Section 4.2 and read Section 4.3 up to but NOT including Theorem 4.9 (Cramer's Rule). We are not covering Cramer's rule in this course. We are not covering Section 4.5 and will move on to Section 5.1 on Wednesday. The review in Section 4.4 could be useful.
  • Do:
    • In Section 4.2: 25. You should be able to check the answers to problems 13 to 22 easily using the methods in this section.
    • In Section 4.3: 12, 14, and 15.
Wednesday:
  • Study: Read Section 5.1.
  • Do: In Section 5.1, 4bd (for 4b, the characteristic polynomial is $p(\lambda)=-(\lambda-1)(\lambda-2)(\lambda-3)$), 10. (Drat: these are 3bd and 9 in the 4th edition.)
Friday:
  • Study: Finish Section 5.1 and start Section 5.2.
  • Do: In Section 5.1: 9ab and 12. (If you have the 4th edition of the text, these are 8ab and 11.)


Week of February 22 to 26
Assignments Made on:
Monday:
  • Study: Finish Section 5.2. We will not cover Section 5.3. We will also not cover the subsections in Section 5.2 on systems of differential equations or general direct sums. We may do a little of Section 5.4 and then it will be on to Section 6.1.
  • Do: In Section 5.2: 8, 10, 13, and 14. In the 4th edition of the text it is 12 and 13 in place of 13 and 14. I suggest looking at problem 12 (only in the 5th edition). The answer is on the web.
Wednesday:
  • Study: Read Section 5.4.
  • Do: In Section 5.4: 11, 13, 17, and 19. Naturally, it would be good to have a look at 1, 2, and 6 (at least those parts that have answers in the back of the book).
Friday:
  • Study: Read Appendix D (on complex numbers) and Section 6.1
  • Do: In Section 6.1: 4b, 6, 9, 10, 11, and 16a.


Week of March 1 to 5
Assignments Made on:
Monday:
  • Study: We'll finish most of Section 6.2 today. Please note that we may be skipping parts of Section 6.2--6 as we finish up. You will only be responsible for what we cover in lecture.
  • Do: No new written assignment today. However, it would be wise to work some of the parts of problem 2 (in Section 6.2) that have answers in the back of the book. You will certainly need to be able to use the Gram-Schmidt method down the road.

    Wednesday's assignment, Homework number 8, will be the last assignment to be turned in. There will be homework assigned, but it will not be graded. That does not mean that it won't be covered on the final exam.
Wednesday:
  • Study: Read Section 6.2 and start Section 6.3. We are not covering least squares approximations and minimal solutions in Section 6.3.
  • Do: In Section 6.2: 7, 8, 11, 17, and 19c.
Friday:
  • Study: Finish Section 6.3 and 6.4
  • Do: In Section 6.3: 8, 9, 11, 12, and 13.


Week of March 8 to March 10
Assignments Made on:
Monday:
  • Study: Read the revelant parts of Section 6.5. Recall that we are no longer collecting homework, but this material could easily find its way onto the final.
  • Do:
    • In Section 6.4: 2a and 9.
    • In Section 6.5: 2abd (in part (d) the characteristic polynomial is $-(\lambda+2)^2(\lambda-4)$), 3, 10, and 11.
Wednesday:
  • Study: No New Material Today. Good luck on the final.
  • Do: No more assignments.
Friday:
  • Study:
  • Do:


Dana P. Williams
Last updated March 10, 2021 12:04:08 EST