MTH 122 Elementary Linear Algebra Fall 2014 Dr. Gisela Ahlbrandt

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1 MTH 122 Elementary Linear Algebra Fall 2014 Dr. Gisela Ahlbrandt Required Text: Elementary Linear Algebra A Matrix Approach 2e by Spence, Insel, Friedberg Second Edition Graphing Calculator capable of doing matrix operations required, TI84, TI86, TINSpire strongly recommended Web supplement: Course Description Vectors and matrices, operations on matrices, determinants, systems of linear equations, linear independence, linear transformations, applications. Prerequisites: MATH105 with a minimum grade of C or MATH120 with a minimum grade of D- or MATH112 or placement Course Objectives The major goal of the course is to study the properties of vectors, vector spaces, linear transformations, matrices, the connection to the theory of solving systems of linear equations, independence and basis. The material provides a first exposure to abstract mathematical argumentation (proofs), which is so typical for upper level mathematics courses. Learn the use of technologies to solve standard linear algebra problems. Topics covered We will cover most material in the textbook. Unit 1. Matrices and vectors, linear combinations, systems of linear equations, Gaussian elimination, the inverse of a matrix, linear transformations. Applications (Sections , , 6.1,) Unit 2. Determinants, vector spaces, subspaces, basis and dimension, coordinate systems. (Sections , , ) Unit 3. Eigenvalues and Eigenvectors, diagonalization of matrices, the geometry of vectors, orthogonal vectors, orthogonal projections, Least squares approximations.(sections , ) Class organization and grading Homework is assigned for each section and the assignments are due on the day after the section is covered and there is a penalty for late work. The points for homework are assigned mainly for effort. A student may thus receive full points without having the homework totally correct. I mostly assign the odd problems from the sections and their solutions are contained in the solution manual,

2 which I recommend. I do not expect that you do every assigned problem, in particular if you feel it turns into busy work, do a representative sample of the problems, but make sure you know how to do them. I collect the homework to make sure that all students have worked on the problems and keep up with the class work as we cover the material. Students will be asked on occasion to present their solutions to the class for discussion. Some in-class activities will be based on students working together in groups and peer reviewing their work. We will also have several quizzes. They are usually given at the beginning of the class period; so make sure you come on time. Quizzes cannot be made up after they are taken in class. Only the five best quizzes will be averaged and the remaining scores will be dropped. In case a quiz was missed this allows for a missed class. If a quiz is assigned as a take-home, you are allowed to work together and get help from the tutor center. We will have two in-class tests and a final exam. All tests are cumulative since the material naturally builds up in layers and later concepts rely on the understanding of earlier ideas. Rules during exams: Use black or blue pen or pencil. Don't leave the room during a test. You can leave the room after you are done. If you leave while other people are still writing, close the door quietly. No hats with visors during tests and quizzes, baseball hats need to be turned to the back. Come on time! If you do oversleep, come in even if it is half way through the test, we will deal with it. Grades The grade will be computed by averaging the scores on the 2 tests, the final, the homework and the 5 best quizzes with equal weights. In case it will help your score the final exam will count twice the weight of the other components. The letter grades are assigned on a straight scale. Grade percentage Grade percentage A 93% and up C 73% A- 90% C- 70% B+ 87% D+ 67% B 83% D 63% B- 80% D- 60% C+ 77% E less than 60%

3 My office is in 515 K Pray-Harrold; my office phone is My home phone is (Please, do not call me at home after 8 PM) You can leave a message on my home answering machine. The best way to contact me is to write me an message. My address is Gisela.Ahlbrandt@emich.edu My WWW-Page is Office hours Walk-in : TR: 8:30 9:20 AM, 12:30 1:50 PM Other hours by appointment Academic Honesty I expect all students to abide by the University s code of conduct, and in particular to abide by rules concerning academic honesty. In order to assess how the class is going and what you have learned, I need to see your own work: your own words and the details of your own computations. You may work with other students or math tutors on your assignments, but you must do an independent write-up. I will give failing grades for academic dishonesty. Students with Disabilities: Eastern Michigan University has a tradition of providing access to education for students with disabilities that began long before the enactment of federal or state law governing accommodations. To see an outline of the accommodation information for faculty and students provided by the Disability Resource Center, visit the DRC homepage: Important Notice for Foreign Students: Foreign students should be aware of the requirements of the SEVIS program. For information about maintaining your visa, go to

4 Tentative Schedule for Math 122 Dr. Ahlbrandt Fall 2014 Week 1 9/2 Week 2 9/9 Tuesday Thursday No class Topic: Topic: 6.1 Topic: Week 3 9/16 Topic: Topic: Week 4 9/23 Topic: Topic: Week 5 9/30 Topic: Topic: 3.1, Week 6 10/7 Topic: Review 10 Test 1 11 Week 7 10/14 Topic: Topic: Week 8 10/21 Topic: 4.2, Topic: Week 9 10/28 Topic: Topic: Week 10 11/4 Topic: Review 18 Test 2 19 Week 11 11/11 Topic: Topic: Week 12 11/18 Topic: Topic: Week 13 11/25 Topic: Thanksgiving Week 14 12/2 Topic: Topic: Week 15 12/9 Topic: Topic: Review 28 Week 16 12/16 Final exam 11:00-12:30 PM

5 Assignments for Math 122 Fall 2014 Dr. Ahlbrandt For each section you should read the section, learn the definitions and work through the examples in the text. The problems below are the ones relevant for us. It is assumed that you know how to solve them and they may appear on quizzes or tests. This is the list of relevant problems from each section from Elementary Linear Algebra, A Matrix Approach 2 nd Edition, by Spence, Insel and Friedberg 1.1: 1, 3, 5, 17, 23, 33, : 1, 3, 5, 9, 17, 19, 21, 23, odds, 71, 73, : 3, 5, 13, 17, 45, all odds 1.3:1, 5, 9, odds, odds Write all general solutions also in vector form and say if it s a line in 2 or 3 space. 1.4: 1-11 odds, 17, 19, 21, 27, 29, 35, 37, 43, 47, 49, 51, all odds 1.6: 1-7 odds, 11, odds, all odds, 65, : 1-25 odds, 31, 33, 35, 39, 41, 43, 45, 51, 53, 55, all, : 1-19 odds, odds, all odds 2.3: 1-5 odds, 9, odds, all odds 2.4: 1-9 odds, odds, 27, 29, all odds, 57, :1-11 odds, odds, all odds, odds, : 1-5 odds, odds, odds, odds, all odds, 63, all odds, Chapter 1 Review problems starting on page 87: 9, 49, Also the true-false questions from sections which we skipped: 1.1: all odds, 1.2: all odds, 1.3: all odds, 1.4: all odds Chapter 2 Review problems starting on page all odds, 45, 46, 48, 50, 54, 56, 58, 60, : 1, 3, 13, 21, 23, 25, 33, 37, all odds 3.2: 5, 11, 13, 15, 27, all odds, 63 (use the calculator to find the determinants), 75, 1-11 all odds, 29, all odds. 4.1: 1, 7, 13, 21, 29, 41, all odds, 67, 69, 73, 81, 83, 91, : 5, 9, 19, all odds, 4.3: 3, 7, 15, 19, 27, 35, all odds, 65, :1, 3, 9, 13, all odds, all odds, 75, 79, 4.5: 1, 5, 11, 15, all odds, 43, 49, 51, all odds 83, : 5, 11, 17, 23, all odds, 61, 67, : 1, 5, 9, 13, 19, 21, 25, all odds, 51, 55 Note there is a typo in 25. It should say n = 2. We only cover 7.4 through Example 4 on page 525. We may come back to this later if we have time. 7.4: 1, 4-10 all, all Chapter 3 Review problems starting on page 222: Chapter 4 Review problems starting on page 286: 1-30 all, 33, 47, 48 Chapter 7 Review problems starting on page 547: 1-4, 12, 13, 16, 19-21,

6 5.1: 3, 19, 25, 27, 33, 35, all 5.2: 1, 3, 13, 15, : 1, 5 We only cover section 5.5 through the middle of page : odds, 30, : 3, 5, 13, 21, all We only cover section 6.2 through the middle of page : 1, 5, 11, 15 Make sure you use the method from this section. I will put a problem on the test that cannot be solved with the regression function on your graphing calculator. Review problems chapter 5 starting on page 355: 1-19 all, 23, 38 Review problems chapter 6 starting on page 481: 1-5 all, 30, 42

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MTH 215: Introduction to Linear Algebra Fall 2017 University of Rhode Island, Department of Mathematics INSTRUCTOR: Jonathan A. Chávez Casillas E-MAIL: jchavezc@uri.edu LECTURE TIMES: Tuesday and Thursday,