MAT 414 Linear Algebra IISection 1 (3229)

SB 306A WeFr 10:50-12:05Salem State University

Instructor: Dr. Brian TraversOffice: Sullivan Building 308BPhone Number: 978.542.6339Email: btravers@salemstate.edu

Webpage: http://btravers.weebly.comOffice Hours: Mo 9-11, WeFr 9:30-10:30, We 12:30-1:30 or by appointment

Required text : Linear Algebra with Applications, 1st edition by Jeffrey Holt.

Overview: 3 credit(s) This course is a continuation of Linear Algebra I. Topics may includeinner product spaces, canonical forms, quadratic forms, similarity, Hermitian, unitary, and normaltransformations. Three lecture hours per week.Prerequisite: MAT 304A.

Grading: There will be 2 in class exams, homework sets and a final exam. They are tentativelyscheduled for October 2nd and November 6th. They will each be worth 25% towards your finalgrade. The final exam is worth 30% and is on Thursday, December 17th at 11 AM. Homework willmake up the final 20% of the grade.

Homework: Homework will be collected approximately every other Friday. The sections sectionsdue on a particular assignment are those that are completed through the class before the due date.You may work with others on these homework assignments, but each student must write their ownsolutions individually. Detailed solutions will be posted on my webpage after the due date.

Attendance Policy: All students are expected to be familiar with the academic regulations,including those regarding Academic Integrity, for Salem State University as published in the uni-versity catalog. In addition, each student is responsible for completing all course requirements andfor keeping up with all that goes on in the course (whether or not the student is present). If youare going to miss a class, I expect an email or a call to my office before class begins. If you contactme ahead of time (other than unexpected situations that can be verified) then the absence will beexcused. If you do not contact me ahead of time then the absence will be unexcused. If you havean unexcused absence on the day of an exam, you will receive a zero for that grade. All unverified“excused” absences after the second one will be considered unexcused. For each unexcused absence,your final grade will be docked in the following manner:

No. of Absences Total Points Lost

1 12 1 + 2 = 33 1 + 2 + 3 = 6

and so forth

Note: For exams, arrangements must be made at least 24 hours in advance in orderfor an absence to be excused.

University Policy Statement: Salem State University is committed to providing equal access tothe educational experience for all students in compliance with Section 504 of The Rehabilitation Actand The Americans with Disabilities Act and to providing all reasonable academic accommodations,aids and adjustments. Any student who has a documented disability requiring an accommodation,aid or adjustment should speak with the instructor immediately. Students with Disabilities whohave not previously done so should provide documentation to and schedule an appointment withthe Office for Students with Disabilities and obtain appropriate services.

In the event of a university declared critical emergency, Salem State University reserves the rightto alter this course plan. Students should refer to www.salemstate.edu for further information andupdates. The course attendance policy stays in effect until there is a university declared criticalemergency. In the event of an emergency, please refer to the alternative educational plans for thiscourse located at http://btravers.weebly.com. Students should review the plans and gather allrequired materials before an emergency is declared.

Global Goals

This course is intended to provide you with an understanding of

• the appropriate linear algebra approach to be applied to practical situations

• the requirements, limitations and validity of such approaches in these practical situations

• the relationship between a matrix and the geometric implications of the associated lineartransformation

• how linear algebra theorems and results impact every day life

Instructional Objectives

By the end of the semester, you should be able to :

• find eigenvalues, eigenvectors and diagonalization of a given matrix134

• put a matrix into Jordan canonical form 134

• understand orthogonality and perform the Gram-Schmidt orthonormalization process to forman orthogonal basis 134

• factor matrices using single value decomposition 134

• use linear transformations , find kernels and ranges, and describe matrices geometrically 234

• understand norms and inner product spaces 234

• connect the previous topics of the course to applications, including quadratic forms and leastsquares approximations 34

Miscellaneous

• I expect you to do all of the homework problems. If you are having trouble, you can come tome for help or you can go to the Math Lab (Sullivan Building 306).

• Believe it or not, it is actually helpful to read the textbook. If you read the material, itwill reinforce the topics covered in class. It is more beneficial, in my experience, to read thesection before we cover it so that you know where you have questions ahead of time.

• Please turn off the ringers on all cell phones and pagers before coming to class.

1Exam 12Exam 23Final Exam4Homework

Homework Problems

Section Problems Problems To Be Submitted

8.1 2–8, 14–16, 22, 26–34, 46–56, 62, 66 8, 14, 26, 32, 34, 62, 66

8.2 2–12, 16–20, 24–28, 38–46, 48, 54, 56 2, 6, 10, 18, 26, 48, 56

8.3 16–24, 30–40, 50–58, 62, 66 20, 24, 30, 36, 40, 62, 66

8.4 2, 6–14, 22–26, 32 10, 14, 18, 32

8.5 2–12, 14, 22–28, 36, 40, 48 10, 14, 36, 40, 48

6.1 2–4, 12–16, 22–28, 38–46, 58, 60 12, 16, 22, 28, 58, 60

6.3 2–26, 30, 40–46 16, 24, 26, 30, 46

6.4 2, 6, 12–16, 20, 32–40, 44, 46 12, 16, 40, 44, 46

Jordan Distributed Later Indicated Later

Exam 1 tentatively scheduled for October 2nd

9.1 2–8, 12–16, 20, 24–28, 40–48, 52, 56, 60 4, 8, 16, 24, 52, 60

9.2 2–12, 16, 18, 32–48 12, 16, 18, 46, 48

9.3 2, 6–10, 14–24, 28, 34, 42–48 8, 14, 20, 34, 48

9.4 2–10, 14, 18–20, 26–34, 38 6, 10, 14, 18, 38

10.1 2–8, 16-24, 28, 42–50, 58, 64 2, 8, 16, 22, 28, 58, 64

10.3 2, 8–12, 16, 20, 30–34, 40 2, 8, 12, 20, 40

Exam 2 tentatively scheduled for November 6th

11.1 2, 6–10, 14, 16, 20, 22, 36–44 2, 10, 14, 20, 42, 44

11.2 2–10, 14–22, 32–36 2, 10, 14, 20, 22

Homework Comments

• Either write the problem out before starting or include enough of the problem in the expla-nation so that the reader can understand why you are doing what you are doing.

• Anything I cannot read is wrong, so make sure all work is legible. This extends to a followableargument and is not limited to handwriting. If I cannot follow the rationale of the solution,even if you have the correct ‘math’, I will mark it incorrect.

• Only write on one side of the paper so I have room for comments.

• Staple your pages together before submission.

• You must give full explanations, justifications and conclusions, even if the text does notspecifically ask for it. I am asking for that now for each problem.

• Since I am posting solutions after I collect the assignment, no late assignments will be ac-cepted. If you are going to miss a class when a homework set is due, you must make arrange-ments to get the assignment to me before class to receive credit.