Math 221 - Linear Algebra - Fall 2023
Location: Mathematics/Psychology 103
Time: TTh 1:00pm-2:15pm

Course Information

Instructor: Dr. Matthew D. Kvalheim
Office: Math/Psych 432
Phone: 410-455-2432
Office Hours: TTh 11:45am-12:45pm
Prerequisites: Math 141, 151 or 380, with a C or better, or approval of instructor
Course Textbook: Linear Algebra and Its Applications by David C. Lay and Steven R. Lay and Judi J. McDonald, 6th edition, Pearson, 2021.
MyLab: The course will use Pearson's MyLab software, which comes with both the eText and the interactive textbook. You will access MyLab via the course's Blackboard Ultra shell.
Course Description
Linear algebra is ubiquitous in disciplines scientific and social and is a thriving discipline on its own with branches in applied science and more theoretical analysis. In this course we will begin with systems of linear equations and their solutions and then start to abstract these techniques and create a general system of vector spaces from which more general manipulations are possible. We will ground the theory in many examples.


Grading Policy
Your grade will be broken down as 45% for three in-class exams (15% each), 30% for the final exam, and 25% for homework. There will be approximately 11 weekly assignments, 2 of which may be dropped. Since you may drop up to 2 homework assignments, I will not be allowing any late homework. You are still responsible for the material on the homework even if it is not turned in. You must clear a missed exam (allowed only for exigent circumstances) with me prior to the test day. In the case of an emergency, you must be able to provide verification (e.g., a doctor's note).

Letter grades follow the traditional scale (90's are A's, 80's are B's, etc.) Participation will be to a student's benefit. Blackboard will be used to post grades.

Academic Integrity Statement
By enrolling in this course, each student assumes the responsibilities of an active participant in UMBC's scholarly community in which everyone's academic work and behavior are held to the highest standards of honesty. Cheating, fabrication, plagiarism, and helping others to commit these acts are all forms of academic dishonesty, and they are wrong. Academic misconduct could result in disciplinary action that may include, but is not limited to, suspension or dismissal. To read the full Student Academic Conduct Policy, consult the UMBC Student Handbook, the Faculty Handbook, the UMBC Integrity webpage .
Course Help
Spend 2-3 hours per credit hour in class doing the following:
Tentative Course Schedule

Day and Date Topic Homework
Thurs Aug 31 Introduction and 1.1-Systems of Linear Equations
Tues Sept 5 1.2-Row Reduction and Echelon Forms
Thurs Sept 7 1.3-Vector Equations
Tues Sept 12 1.4-The Matrix Equation Ax=b Due HW1
Thurs Sep 14 1.5-Solution Sets of Linear Systems
Due HW2
Tues Sept 19 1.7-Linear Independence
Thurs Sept 21 1.8-Introduction to Linear Transformations Due HW3:
Tues Sept 26 1.9-The Matrix of a Linear Transformation
Thurs Sept 28 2.1-Matrix Operations Due HW4
Tues Oct 3 Exam #1
Thurs Oct 5 2.2-The Inverse of a Matrix
Tues Oct 10 2.3-Characterizations of Invertible Matrices
4.1-Vector Spaces and Subspaces
Thurs Oct 12 4.2-Null Spaces, Column Spaces, and Linear Transformations Due HW5
Tues Oct 17 4.3-Linearly Independent Sets; Bases
4.4-Coordinate Systems
Thurs Oct 19 4.5-The Dimension of a Vector Space Due HW6
Tues Oct 24 3.1-Introduction to Determinants
Thurs Oct 26 3.2-Properties of Determinants Due HW7
Tues Oct 31 Exam #2
Thurs Nov 2 5.1-Eigenvectors and Eigenvalues
Tues Nov 7 5.2-Characteristic Equation
Thurs Nov 9 5.3-Diagonalization Due HW8
Tues Nov 13 6.1-Inner Product, Length, and Orthogonality
Thurs Nov 16 6.2-Orthogonal Sets Due HW9
Tues Nov 21 6.3-Orthogonal Projections
Thurs Nov 23 Thanksgiving Break
Tues Nov 28 6.5-Least Squares
Thurs Nov 30 6.6-Machine Learning and Linear Models Due HW10
Tues Dec 5 Due HW11
Thurs Dec 7 Exam #3
Tues Dec 12 Last Day of Class - RECAP
Wed Dec 13 Reading day
Tues Dec 19 FINAL EXAM 1:00-3:00pm (SHER 145)
Accessibility and Disability Accommodations, Guidance and Resources
Accommodations for students with disabilities are provided for all students with a qualified disability under the Americans with Disabilities Act (ADA & ADAAA) and Section 504 of the Rehabilitation Act who request and are eligible for accommodations. The Office of Student Disability Services (SDS) is the UMBC department designated to coordinate accommodations that creates equal access for students when barriers to participation exist in University courses, programs, or activities.

If you have a documented disability and need to request academic accommodations in your courses, please refer to the SDS website at for registration information and office procedures.

SDS email:

SDS phone: 410-455-2459

If you will be using SDS approved accommodations in this class, please contact the instructor to discuss implementation of the accommodations. During remote instruction requirements due to COVID, communication and flexibility will be essential for success.

Sexual Assault, Sexual Harassment, and Gender Based Violence and Discrimination

UMBC Policy in addition to federal and state law (to include Title IX) prohibits discrimination and harassment on the basis of sex, sexual orientation, and gender identity in University programs and activities. Any student who is impacted by sexual harassment, sexual assault, domestic violence, dating violence, stalking, sexual exploitation, gender discrimination, pregnancy discrimination, gender-based harassment, or related retaliation should contact the University’s Title IX Coordinator to make a report and/or access support and resources. The Title IX Coordinator can be reached at or 410-455-1717.

You can access support and resources even if you do not want to take any further action. You will not be forced to file a formal complaint or police report. Please be aware that the University may take action on its own if essential to protect the safety of the community.

If you are interested in making a report, please use the Online Reporting/Referral Form. Please note that, if you report anonymously, the University’s ability to respond will be limited.

Notice that Faculty and Teaching Assistants are Responsible Employees with Mandatory Reporting Obligations

All faculty members and teaching assistants are considered Responsible Employees, per UMBC’s Policy on Sexual Misconduct, Sexual Harassment, and Gender Discrimination. Faculty and teaching assistants therefore required to report all known information regarding alleged conduct that may be a violation of the Policy to the Title IX Coordinator, even if a student discloses an experience that occurred before attending UMBC and/or an incident that only involves people not affiliated with UMBC. Reports are required regardless of the amount of detail provided and even in instances where support has already been offered or received.

While faculty members want to encourage you to share information related to your life experiences through discussion and written work, students should understand that faculty are required to report past and present sexual harassment, sexual assault, domestic and dating violence, stalking, and gender discrimination that is shared with them to the Title IX Coordinator so that the University can inform students of their rights, resources, and support. While you are encouraged to do so, you are not obligated to respond to outreach conducted as a result of a report to the Title IX Coordinator.

If you need to speak with someone in confidence, who does not have an obligation to report to the Title IX Coordinator, UMBC has a number of Confidential Resources available to support you:

Retriever Integrated Health (Main Campus): 410-455-2472; Monday – Friday 8:30 a.m. – 5 p.m.; For After-Hours Support, Call 988.

Center for Counseling and Well-Being (Shady Grove Campus): 301-738-6273; Monday-Thursday 10:00a.m. – 7:00 p.m. and Friday 10:00 a.m. – 2:00 p.m. (virtual) Online Appointment Request Form

Pastoral Counseling via The Gathering Space for Spiritual Well-Being: 410-455-6795;; Monday – Friday 8:00 a.m. – 10:00 p.m.

Other Resources

Women’s Center (open to students of all genders): 410-455-2714;; Monday – Thursday 9:30 a.m. – 5:00 p.m. and Friday 10:00 a.m. – 4 p.m.

Shady Grove Student Resources, Maryland Resources,

Child Abuse and Neglect

Please note that Maryland law and UMBC policy require that faculty report all disclosures or suspicions of child abuse or neglect to the Department of Social Services and/or the police even if the person who experienced the abuse or neglect is now over 18.