MATH 333: Homework Assignments
Unless announced otherwise, homework will be due on Wednesday each week. Turn in your assignment to me (in class or my office) before 4:00 PM each Wednesday.
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| Set | Homework Problems | Reading Assignment | Due Date | ||
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| Read Appendix A, B, C, D, and Sections 1.1-1.2 | |||||
| NOTE: The first assignment will be due Friday, instead of Wednesday. Sec. 1.1: 1, 2(a,b) (For #1, at least two of the pairs are not parallel. Use "proof by contradiction" for at least one of these.) Sec. 1.2: 1, 2, 7, 11, 12, 13, 18, 22 (For #1, if false give a reason why.) Here is an example of a proof to help you. This is actually problem #12. This should help you know how your proof for this problem and similar problems should look. |
Read Sections 1.3, 1.4 | ||||
| Sec. 1.2: 9 Sec. 1.3: 1, 2(a,b,e), 3, 5, 8(a,b,d,e), 11, 20, 22 (For #1, if false give a reason why.) Extra Problem: "If r is a positive real number, then there is a unique real number x such that x3=r." (Use the "Uniqueness Proof" technique we learned in class to prove this proposition. You must do this problem. It is not optional.) |
Read Sections 1.5 | ||||
| Sec. 1.4: 1, 2(a), 3(c), 4(a), 5(g), 7, 8, 11, 13 (For #1, if false give a reason why. For 3, 4 and 5, a simple 'yes' or 'no' is insufficient. You must find a linear combination if one exists, or prove one does not exist if it doesn't.) Sec. 1.5: 1, 3, 7, 9, 10, 17(For #1, if false give a reason why.) |
Read Sections 1.6 | ||||
| Exam 1 is on Friday, Sept. 28: The exam will cover all of Sections 1.1-1.6 of the textbook. It will be similar to the homework. To practice for the exam, review the homework problems, do some extra problems similar to the homework problems, and know all of the definitions and theorems. Here are the review sheet, practice exam, and solutions. We will have a review in class on Wednesday. Sec. 1.6: 1, 2(a), 3(a), 4, 5, 9, 12, 14, 16 (For #1, if false give a reason why. For 2 and 3, a simple 'yes' or 'no' is insufficient. You must justify your answer. Note that 4 and 5 are EASY to justify in a single sentence.) |
Read Sections 2.1 | ||||
| NOTE: This assignment will be due Friday, instead of Wednesday. Sec. 2.1: 1, 2, 4, 5, 9(a,b,e), 10, 12, 16, 17, 18 (For #1, if false give a reason why. Make sure you justify your answer to #12 and #18.) |
Read Sections 2.2 | ||||
| Sec. 2.2: 1, 2(a,d,g), 3, 4, 5(a,b,e,f,g), 8, 9, 15(a,b) (For #1, if false give a reason why.) Sec. 2.3: 2, 8 (just prove Thm. 2.10, don't do the rest), 9, 11, 12 (Recall T0 denotes the zero transformation, i.e. T0(x)=0 for all x.) |
Read Sections 2.3, 2.4 | ||||
Corrections |
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Friday, October 19 |
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| Sec. 2.3: 1, 3, 4(a,b), 7 (For #1, if false give a reason why.) Sec. 2.4: 1, 2(a,d,e), 4, 5, 6, 7 (For #1, if false give a reason why.) Read and UNDERSTAND what #15 and #17 of Sec. 2.4 are telling you, but you don't have to do them (unless you want to.) They will be helpful to you later. I moved #3, 13, 14 from Section 2.4 to next week's assignment. Please hand them in next week. |
Read Sections 2.5, 3.1 | ||||
| Exam 2 is on Friday, Nov. 2: The exam will cover all of Sections 2.1-2.5 of the textbook. It will be similar to the homework. To practice for the exam, review the homework problems, do some extra problems similar to the homework problems, and know all of the definitions and theorems. Here are the review sheet, practice exam, and solutions. We will have a review in class on Wednesday. Sec. 2.4: 3, 13, 14 Sec. 2.5: 1, 2(a,b), 3(b,d), 5, 6(b), 9 (For #1, if false give a reason why.) Help: For Sec. 2.4 #13 and Sec. 2.5 #9 you will need the definition of "equivalence relation", which is given on page 551. It simply means that two things are not only related, but they are actually equivalent. Click here for a few examples. |
Read Sections 3.2, 3.3 | ||||
| Sec. 3.1: 1(not h), 2(don't do "A into B"; it involves a column operation.), 3, 5 (For #1, if false give a reason why.) Sec. 3.2: 1(a,c,d,h,i), 2(a,c,g), 3 (For #1, if false give a reason why.) We will NOT be using column operations at this time, only row operations. I've attempted to not assign any problems that require column operations. Use only elementary row operations unless you absolutely have to use column operations. Read and UNDERSTAND what #12 of Sec. 3.1 is telling you, but you don't have to do it (unless you want to.) It will be helpful to you later. |
Read Sections 3.3, 3.4 | ||||
| Sec. 3.2: 1(b,g), 5(a,c,e), 6(a,c), 7, 8 (For #1, if false give a reason why.) Sec. 3.3: 1, 2(a), 3(a, use Theorem 3.9), 4(a), 8(a), 9 (For #1, if false give a reason why. For #2 and #8, use matrices and row reduction to rref.) |
Read Sections 4.1-4.2 | ||||
Corrections |
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Monday, November 19 |
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...Yeah right! Have a great and safe break! |
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| Problem A: Prove this is part of the Big Theorem: "Let B be any row echelon form of an nxn matrix A. Then every column of B is a pivot column if and only if B has no zeros along the diagonal." Problem B: This is an extra problem you'll need to do for this assignment. Hint: There are 3 categories Sec. 3.4: 1(not a,f), 2(a,e), 5 (For #1, if false give a reason why. For #5, you will need to use Theorem 3.16.) Sec. 4.1: 2(a), 5, 7, 9 (For a review of complex numbers, you can read Appendix D.) (Use only the definition of 2x2 determinants on page 200 for all computations AND proofs from Sec. 4.1.) Sec. 4.2: 1(not a), 2, 3, 7, 9, 13, 21, 25 |
Read Sections 4.3, 4.4, 5.1, 5.2, and Appendix D | ||||
Click here to complete the evaluation |
completed by Monday, December 10 |
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| Sec. 4.3: 1(a,b,c,d,e), 9, 10, 12 Sec. 4.4: 1 (We are skipping a lot here. Section 4.4 gives a nice summary, and the examples are in Sections 4.1-4.3. There are A LOT of things that may be of interest to you that we are skipping, such as the AMAZING Cramer's Rule as well as using determinants to find areas and volumes of parallelograms and parallelepipeds. Hopefully you learned some of this stuff in ELA, but there is also some new stuff in these sections. Read as much as you can/want.) Sec. 5.1: 1, 2(a,c,d), 3(b,c,d), 4(d,h), 5, 8(c), 9, 15 (HINT for #5: We proved in class the equivalent of this theorem in terms of matrices. For #15: T m just means T composed with itself m times. For example, T 3(x)=T(T(T(x))).) Sec. 5.2: 1(a-f), 2(a,b,e), 3(a,b), 8 |
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Exam |
The Final Exam is on Friday, December 14, 8:00-11:00 am, in class (Sturges 113): We will have a review in class on Monday. The exam is a two part cumulative exam and will be similar to the homework. To practice for the exam, review the homework problems, do some extra problems similar to the homework problems, and know all of the definitions and theorems. Here are the resources:
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