Sections:
Books:
Syllabus for Math 321 (32505).
Syllabus version from January 17th, 2022.
UNM required extra language for Syllabus.
Main book: Jim Hefferon, Linear Algebra,
Free book available in electronic form at the Author's website
(all information about licenses is given there). You can also purchase paper copy for less than $22 (current price, December 2019) on Amazon.
Here is the direct link to the version of the book which is used as a source of homeworks problems.
Optional reading: Introduction to Linear Algebra book, available at Kenneth Kuttler web-site,
Here is a direct link to the text of the book.
Office hours:
TR 12:30-13:45. Room: SMLC 220.
How grades are assigned?
All homeworks: 100 points (only few randomly chosen problems from the homework will be graded).Two midterm exams: 100 points each (100+100 points).
In class quizzes: 50 points.
Final exam: 200 points.
Total: 550 points.
Lowest bondaries for grades (not higher than):
A = 495, B = 440, C = 380, D = 330.
No late HWs are accepted after graded HW is returned. Even before for a late submission you shall get -1 point from the grade.
| HW # | Homework problems | Due date |
|---|---|---|
| - |
Cumulative Final Exam on Tuesday, May 10th, 7:30-9:30am, usual classroom. One page two sides of reference sheet is allowed (as usual, no problems solutions) Training set of problems (don't forget about ALL exams, ALL quizzes(!); other problems from HWs and examples in the text might be helpful): 0) One.III.1, p. 54: 1.12 (a,b,d); One.III.2, p. 62: 2.27; 1) Two.III.1, p. 118: 1.18 (a,b), 1.19 (a,b), 1.20 (a,b); 2) Three.I.1, p. 172: 1.12 (b), 1.15, 1.16, 1.17 (a,c,d); 3) Three.II.2, p. 200: 2.23 (a), 2.27; 4) Three.IV.4, p. 252: 4.15 (a,c,d), 4.16; 5) Three.V.1, p. 257: 1.7, 1.9 (a,d), 1.10 (a,c), 1.21 (a); 6) Four.I.2, p. 321: 1.1, 1.9, 1.10, 1.13, 1.15; 7) Four.III.1, p. 357: 1.14, 1.16 (a,b); 8) Five.II.2, p. 396: 2.6, 2.7 (a), 2.8, 2.11; 9) Five.II.3, p. 405: 3.22 (a,d,e), 3.23 (a,b), 3.24, 3.26(a), 3.30, 3.32; 10) Three.VI.2, p. 275: 2.10(a,b), 2.11, 2.12, 2.15; (in 2.11-12 get orthonormal basis through Gramm-Schmidt). |
- |
| 12-13 |
Quiz10 on Thursday, May 5th (Solution published). Topic: Eigenvalues and eigenvectors (see problem 6 in Exam2). Additional reading (just for fun). MATLAB for Linear Algebra. Three.VI.3, p. 283: 3.11(a,f); Five.II.1, p. 391: 1.7, 1.8; Five.II.2, p. 396: 2.6, 2.7 (a), 2.8, 2.11; Five.II.3, p. 405: 3.22 (a,d,e), 3.23 (a,b), 3.24, 3.26(a), 3.30, 3.32. |
May 6th, 2022, |
| 10-11 |
Quiz08 on Tuesday, May 3rd (Solution published). Topic: Gram-Schmidt ortogonalization process. Quiz09 on Tuesday, May 3rd (Solution published). Topic: Least Squares method (Extra info for least squares, useful for the quiz.). Addition to the homework. Complex numbers. Four.III.1, p. 357: 1.14, 1.16 (a,b); Four.Cramer's Rule, p. 360: 1(a), 2; Three.VI.1, p. 270: 1.6(a), 1.7(a); Three.VI.2, p. 275: 2.10(a,b), 2.11, 2.12, 2.15; (in 2.11-12 get orthonormal basis through Gramm-Schmidt) Three.Line of the Best Feet - read the topic, read the Extra info for the quiz above and do the example there by yourself. |
May 2nd, 2022, end of day. |
| - |
Exam 2 on Thursday, April 21st (Solution published). Topics: all covered material since Exam 1, up to and including Four.III.1. As usual, no calculators or books allowed. You can prepare a page of reference of any formulae etc. you like. Training set of problems for Exam 2: Three.II.2, p. 200: 2.23 (a), 2.27; Three.III.1, p. 211: 1.18, 1.20 (a,b), 1.21(b); Three.III.2, p. 220: 2.14, 2.19; Also review Quiz 05; Three.IV.4, p. 252: 4.15 (a,c,d), 4.16; Three.V.1, p. 257: 1.7, 1.9 (a,d), 1.10 (a,c), 1.21 (a); Three.V.2, p. 265: 2.13, 2.16, 2.28 (a);Have a look at the solution of the quiz 06! Four.I.2, p. 321: 1.1, 1.9, 1.10, 1.13, 1.15; Four.I.3, p. 335: 3.38; Also review the null-space and how to find a basis for the null space for a transformation given by the matrix. Here is an example, study it thoroughly! |
None. |
| 9 |
Quiz06 on Tuesday, April 19th (Solution published). Topic: you will need to be able to change matrix map representation for different bases. Quiz07 on Tuesday, April 19th (Solution published). Topic: determinants. (Yes, double quiz.) Three.V.1, p. 257: 1.7, 1.8 (a,c), 1.9 (a,d), 1.10 (a,c), 1.16, 1.19, 1.21 (a); Three.V.2, p. 265: 2.10 (a,b), 2.11 (a,b), 2.13, 2.15 (a,b), 2.16, 2.28 (a); Four.I.1, p. 321: 1.1, 1.3, 1.4, 1.5 (b), 1.7, 1.9, 1.10, 1.13, 1.15; Four.I.2, p. 326 (read examples in this section): 2.8(a), 2.9, 2.11, 2.20, 2.22; Four.I.3, p. 335: 3.17, 3.19, 3.22, 3.23, 3.29, 3.38; Four.I.4, p. 345: 4.11, 4.13; Four.II.1, p. 350: 1.9(a,c), 1.14 (a,c), 1.19; |
April |
| 7-8 |
Quiz02 on Tuesday, April 5th (Solution published). Topic: Gauss-Jordan reduction method for systems of linear equations. Quiz05 on Thursday, April 7th (Solution published). Topic: you will need to prove that some map is homomorphism by applying the definition and find a matrix representation of the map. Three.II.2, p. 200: 2.21 (a,d), 2.22 (a,b), 2.23 (a), 2.27, 2.31 (a); Three.III.1, p. 211: 1.12 (a,b,c), 1.13 (b), 1.15, 1.16, 1.17, 1.18, 1.20 (a,b), 1.21(b), 1.26 (a-d); Three.III.2, p. 220: (read corollary 2.6) 2.12 (c), 2.13 (b), 2.14, 2.15 (a), 2.16, 2.19; Three.IV.1, p. 226: 1.8 (a,e), 1.15, 1.16, 1.17; Three.IV.2, p. 233: 2.14 (b,c), 2.16, 2.18, 2.24, 2.25, 2.27 (Hint: for the last two problems use induction); Three.IV.3, p. 243: 3.25 (a,c,e), 3.27, 3.40, 3.44, 3.45; Three.IV.4, p. 252: 4.12-14, 4.15 (a,c,d), 4.16, 4.17, 4.18, 4.20, 4.21, 4.29, 4.33 (c,d). |
April |
| - |
Exam 1 on Tuesday, March 8th (Solution published). Topics: all covered material. As usual, no calculators or books allowed. You can prepare a page (one side) of reference of any formulae you like (no problems solution!). You will need to submit this page with your exam. Training set of problems for Exam 1: One.I.3, p. 33: 3.15 (a,c,e), 3.16 (a,b,d); One.II.1, p. 41: 1.2, 1.3; One.II.2, p. 47: 2.20, 2.38, go through proofs in this section; One.III.1, p. 54: 1.12 (a,b,d); One.III.2, p. 62: 2.27; Two.I.1, p. 86: 1.19, 1.22 (a,c,d); Two.I.2, p. 97: 2.22, 2.23; Two.II, p. 109: 1.20 (a,c), 1.21 (b,d); Two.III.1, p. 118: 1.18 (a,b), 1.19 (a,b), 1.20 (a,b); Two.III.2, p. 125: 2.17; Two.III.3, p. 133: 3.18 (b), 3.19 (a,c), 3.21 (a,c,d), 3.23(b,c), 3.26; Three.I.1, p. 172: 1.12 (b), 1.15, 1.16, 1.17 (a,c,d); |
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| 6 |
Three.I.1, p. 172: 1.12 (b), 1.15, 1.16, 1.17 (a,c,d), 1.18, 1.30, 1.37; Three.I.2, p. 181: 2.9 (a,b,d), 2.12 (a,c,d), 2.18; Three.II.1, p. 188: 1.18 (a,c,d), 1.19 (b,c), 1.20, 1.22, 1.23, 1.29, 1.30. |
March |
| 5 |
Quiz03 on Tuesday, March 1st (Solution published). Topic: Linear dependence and independence. Quiz04 on Tuesday, March 3rd (Solution published). Topic: Vector Spaces and Linear Systems (review Tuesday's lecture on columns relations, etc.). Two.III.1, p. 118: 1.18 (a,b), 1.19 (a,b), 1.20 (a,b), 1.21, 1.23, 1.25 (a,c), 1.28 (a,b), 1.34; Two.III.2, p. 125: 2.16, 2.17, 2.18 (a,c), 2.21, 2.22, 2.23, 2.26; Two.III.3, p. 133: 3.16 (a,c,e), 3.17 (b), 3.18 (b), 3.19 (a,c), 3.20, 3.21 (a,c,d), 3.23, 3.26, 3.37. |
|
| 4 |
One.III.1, p. 54: 1.8 (a,d), 1.10 (a,b,c), 1.12 (a,b,d), 1.15; One.III.2, p. 62: 2.11 (a,b,c,e), 2.21, 2.24; Two.I.1, p. 86: 1.17, 1.18, 1.19, 1.22 (a,c,d), 1.24, 1.25, 1.28 (b,c,e), 1.35(b), 1.38; Two.I.2 (read examples in this section), p. 97: 2.20 (a,b), 2.21, 2.22, 2.23 (b), 2.24 (a,b,d), 2.25 (a,c,e), 2.27 (a,c,e), 2.28, 2.34; Two.II, p. 109: 1.20 (a,c), 1.21 (b,d), 1.22 (a,c), 1.23 (a,b), 1.24 (a,b,d), 1.27, 1.28 (a), 1.35, 1.42 (a). |
February 18th, 2022, |
| 2-3 |
One.I.3, p. 33: 3.15 (a,c,e), 3.16 (a,b,d), 3.18 (a), 3.19, 3.20 (a,c,e), 3.21 (a,d), 3.22; One.II.1, p. 41: 1.2, 1.3; One.II.2, p. 47: 2.11 (a,c,e), 2.12, 2.13, 2.14, 2.15, 2.20, 2.25, 2.38. |
February |
| 1 |
Quiz01 on Thursday, One.I.1, p. 9: 1.17 (a,b), 1.18 (a-f), 1.19, 1.20, 1.22, 1.25, 1.28, 1.33; One.I.2, p. 20: 2.15, 2.16, 2.18 (a,d,e), 2.19 (a,c), 2.20 (a,b), 2.23, 2.24, 2.27(a,b). |
January 25th, 2022, class time. |