MATH 332, section 01: Elementary Linear Algebra
Homework Assignments
NOTE: Homework assignments will be posted weekly, one week before the due date. It is your responsibility to check this page and obtain the assigned problems.Homework hints and discusion: Visit the course discussion forums on Blackboard, where you can discuss unclear examples, homework problems, lecture questions, etc. with your peers. I will watch the forums regularly and mediate as necessary. Try reading the discussions at least once a week, and posting a question or answering your fellow student's question at least once every other week. You will quickly see the benefits of this interaction!
| HW # and due date | Assigned problems (these should be turned in) | Suggested exercies (for practice) |
| HW #1. Due: 8/28. | Section 1.1: #8; Section 1.2: #6, #15, #26; Section 1.3: #1 egh, #2. |
Section 1.1: 3, 11c, 12a; Seciton 1.2: 2, 4, 31, 32; And: Find A and B such that AB is not equal to BA. |
| HW #2. Due: 9/4 (extendible to 1pm, Thursday 9/5). |
Section 1.3: #8e, #12a, #22a; Section 1.4: #8, #13, #18b, #22; |
Section 1.3: 4, 20, 28; Section 1.4: 27, 29; |
| HW #3. Due: 9/11 | Section 1.4: #30, #34, #36; Section 1.5: #3c, #8a, #15, #30. |
Section 1.4: 38-55; Section 1.5: 5, 25, 34. |
| HW #4. Due: 9/18 | Section 1.6: #14, #23; Section 1.7: #7, #32; Section 2.1: #11, #26; Section 2.2: #7, #28a, #29. |
Section 1.6: #4, #10, 18, 20, 22; Section 1.7: 19, 21, 27; Section 2.1: 19c, 34*, 35, 37*; Section 2.2: 17, 21, 35, 36. |
| HW #5. Due: 10/2 (extended to noon on 10/3) |
Section 2.3: #19, #31, #34; Section 4.1: #2, #7, #17; Section 4.2: #2abef, #9b, #11c, #12a. |
Section 4.1: 1,4,5,9,11,23,25,27; Section 4.2: 2,8,18,13,20. |
| HW #6. Due: Thu 10/10 (Drop off to TA's mailbox of TA's office hour) |
Section 4.2: #20. Extra credit: section 4.2, #18 and #19. |
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| HW #7. Due: Thu 10/17 (Drop off to TA's mailbox of TA's office hour) |
Section 4.3: #1bd, #2a, #4a, #10, #12, #24. Section 4.4: #1. |
Section 4.3: 11, 13, 28 (this one refers to Chapter 3 as well). |
| HW #8. Due: Thu 10/24 (Drop off to TA's mailbox of TA's office hour) |
Section 4.4: #5,#6,#8a; Section.4.5:#8,#9c,#16,#20a; Section 4.6: #6, #10. |
Section 4.4: 11, 12, 17b(this one highly recommended for practice); Section 4.5: 10, 11, 12, 13, 14, 18, 19; Section 4.6: 1-5, 18, 19. |
| HW #9. Due: Thu 11/7 (Drop off to TA's mailbox of TA's office hour) |
Section 4.7: #4, #6a, #12a, #13, #14; Section 4.8: #1, #13. |
Sec. 4.7: 3, 7, 10. Section 4.8: 5, 6, 7d, 8d, 15. |
| HW #10. Due: Thu 11/14 (Drop off to TA's mailbox of TA's office hour) |
Section 4.8: #10, #16; Section 4.9: #4, #7cd, #10d; Section 4.12: #4, #6a, #8. |
Sec. 4.9: 5, 6, 15, 17; Sec. 4.12: 11. |
| HW #11. Due: Thu 11/21 (Drop off to TA's mailbox of TA's office hour) |
Section 5.1: #9a, #10a, #11a, #16a, #18; Section 5.2: #2, #12, #32. |
Sec. 5.1: 19, 21, 22, 23, 24; Sec. 5.2: 6, 21, 24, 26-31. |
| HW #12. Due: Tue 11/26 (Due at the end of the day. Homeworks that are typed up may be submitted electronically. **PDF only**) |
Section 6.1: #5ade, #20. Section 6.2: #4a, #16a, #22. Section 6.3: #10a. |
Sec. 6.1: 1, 7, 8, 25, 26; Sec. 6.2: 7, 8, 10, 11. |
Class schedule
| Week | Assigned reading | Tentative topics covered in lectures |
| August 19&21 | Sections 1.1-1.3. | Discussion of course organization and purpose; Introduction to linear systems, Gaussian elimination, Matrices and matrix opearations. |
| Aug 26&28 | Sections 1.3-1.5. | Matrix notation and terminology, matrix operations, relations to linear systems, invertible matrices, elementary matrices. |
| Sep 4th (Monday=Labor Day!) | Sections 1.4 and 1.5. | Discusion of HW#1, Properties of transpose, inverse of transpose, inverse of elementary matrices. |
| Sep 9&11 | Sections 1.6, 1.7, 2.1, 2.2 | Number of solutions of a system of linear equations with proof, more statements equivalent to invertibility, basics on diagonal, triangular, symmetric matrices. Introduction to Determinants and some properties, adjoints (with outlook toward Cramer's rule). |
| Sep 16&18 | Sections 2.1, 2.3, 4.1 | Short proof of Cramer's rule, invertibility and determinants, determinants of products, inverse. Characteristic equations, eigenvalues and eigenvectors, Euclidean n-space and some properties. |
| Sep 23&25 | Section 4.1. |
Monday: Mid-term Exam 1. Exam topics are
those covered on Homework sets 1-4. Wednesday: topics from 4.1. |
| Sep 30 & Oct 2 | Sections 4.1 and 4.2. | Discuss Exam#1 solutions; Topics: general vector spaces, subspaces, with proofs and examples. . |
| Oct 9 (Monday = Fall break!) | End of 4.2 and section 4.3. | Space of solutions of a homogeneous linear system. Linear independence. |
| Oct 14&16 | Sections 4.4, 4.5, (4.6.) | Coordinates, bases, dimension, overview/intro to change of bases. Note: Chapter 3 topics will be interspersed naturally throught chapters 4 and 6. |
| Oct 21&23 | Sections 4.6, and more (TBD) | Change of bases. Coordinate transformations, tbd. |
| Oct 28&30 | Section 4.6, 4.7 (and possibly overview of HW8 solutions) | Wednesday: Mid-term Exam 2. Exam topics are those covered in Homework sets 5-8. |
| Nov 4&6 | Sections 4.8 (large part of it), 4.9, 4.12. | Rank, Nullity, Matrix transformations, linear transformations and the standard matrix of a linear map; Applications to dyanmical systems and Markov chains. |
| Nov 11&13 | Sections 5.1 and 5.2. | Eigenvalues and Eigenvectors. |
| Nov 18&19 | End of section 5.2; Sections 6.1 - 6.2 and parts of 6.3 | Properties of Inner products, Cauchy-Schwarz inequality with proof, Angle between two vectors in an i.p.s., Orthogonal vectors, Properties of length (norm) and distance, Generalized Pythagoras Theorem, Orthogonal complement of a subspace, Properties and examples of Orthogonal complements, Null(A) and Row(A) are orthogonal complements, Finding the basis of an orthogonal complement in the Euclidean space, Orthogonal and Orthonormal sets of vectors, Orthonormal Basis. (From Sections 6.1, 6.2 and 6.3) |
| Nov 25 | (Wed = Thx break!) | Mid-term Exam 3 |