Math 221 - Introduction to Linear Algebra

Spring 2027 - Matthias K. Gobbert

Detailed Schedule - Last Updated 09/28/2026

The chapter and section numbers refer to David C. Lay, Steven R. Lay, Judi J. McDonald, Linear Algebra and Its Applications, 6th edition, Pearson, 2021.
This course is taught in a flipped classroom format. This means that you need to study the material and work the homework before class! Recorded lectures and the textbook are provided for contents delivery and we will use Pearson's MyLab for the online homeworks and quizzes. This homework system includes an interactive eText, a Study Plan, hints ("Help me solve this" and "View an example" with every problem), and (essentially) unlimited number of attempts. In each class meeting, we will address questions on the material inspired by the textbook, lectures, and homework, and then work actively in teams.
The two-digits numbers in homeworks HW x.y, group quizzes GQ x.y, and individual quizzes IQ x.y indicate the section number, that is, Chapter x, Section x.y. There are also a few group quizzes in class labeled GQ x.0, typically on some crucially important basic definition of Chapter x. The abbreviation BQ refers to an individual quiz in Blackboard, the abbreviation IQ refers to an individual quiz in MyLab. The abbreviation GQ refers to a group quiz during class. HW 0 is a required homework to be submitted in Blackboard.

Class	Date	Main Topic	Notes
1	Tu 01/25	Overview, mechanics of the course, GQ0a introductions	Pre-ass., BQ0a, BQ0b, HW0 gen.
		1.1 Systems of Linear Equations, GQ 1.1	HW 1.1, IQ 1.1
2	Th 01/27	1.2 Row Reduction and Echelon Form, HW 0, GQ 1.2	HW 1.2, IQ 1.2
		1.3 Vector Equations, GQ 1.3	HW 1.3, IQ 1.3
3	Tu 02/02	Test 0 (Sections 1.1 through 1.3)
4	Th 02/04	1.4 The Matrix Equation A x = b, GQ 1.0, GQ 1.4	HW 1.4, IQ 1.4
		1.5 Solution Sets of Linear Systems, GQ 1.5	HW 1.5, IQ 1.5
5	Tu 02/09	1.7 Linear Independence, GQ 1.7	HW 1.7, IQ 1.7
6	Th 02/11	1.8 Introduction to Linear Transformations, GQ 1.8	HW 1.8, IQ 1.8
		1.9 The Matrix of a Linear Transformation, GQ 1.9	HW 1.9, IQ 1.9
7	Tu 02/16	Review, GQ 1.0
8	Th 02/18	Test 1 (Chapter 1)
9	Tu 02/23	6.1 Inner Product, Length, and Orthogonality, GQ 6.1
10	Th 02/25	2.1 Matrix Operations, GQ 2.0, GQ 2.1	HW 2.1, IQ 2.1
11	Tu 03/02	2.2 The Inverse of a Matrix, GQ 2.2	HW 2.2, IQ 2.2
12	Th 03/04	2.3 Characterizations of Invertible Matrices, GQ 2.3	HW 2.3, IQ 2.3
13	Tu 03/09	Review, GQ 2.0
14	Th 03/11	Test 2 (Chapters 1 and 2)
	Tu 03/16	Spring Break
	Th 03/18	Spring Break
15	Tu 03/23	4.1 Vector Spaces and Subspaces, GQ 4.1	HW 4.1, IQ 4.1
16	Th 03/25	2.8 Subspaces of Rⁿ, GQ 2.8	HW 2.8, IQ 2.8
		2.9 Dimension and Rank, GQ 2.9	HW 2.9, IQ 2.9
17	Tu 03/30	4.2 Null Space, Column Space, and Linear Transformations, GQ 4.2	HW 4.2, IQ 4.2
		4.3 Linear Independent Sets, Bases, GQ 4.3, GQ 4.0	HW 4.3, IQ 4.3
18	Th 04/01	4.4 Coordinate Systems, GQ 4.4	HW 4.4, IQ 4.4
		4.5 The Dimension of a Vector Space, GQ 4.5	HW 4.5, IQ 4.5
19	Tu 04/06	Test 3 (Chapter 4)
20	Th 04/08	3.1 Introduction to Determinants, GQ 3.1	HW 3.1, IQ 3.1
21	Tu 04/13	3.2 Properties of Determinants, GQ 3.2	HW 3.2, IQ 3.2
22	Th 04/15	5.1 Eigenvectors and Eigenvalues, GQ 5.0, GQ 5.1	HW 5.1, IQ 5.1
		5.2 The Characteristic Equation, GQ 5.2, PQ 5.1	HW 5.2, IQ 5.2
23	Tu 04/20	5.3 Diagonalization, GQ 5.3, PQ 5.2	HW 5.3, IQ 5.3
24	Th 04/22	Review, 5.5 Complex Eigenvalues, PQ 5.3
25	Tu 04/27	Test 4 (Chapters 3 and 5)
26	Th 04/29	6.1 Inner Product, Length, and Orthogonality	HW 6.1, IQ 6.1
		6.2 Orthogonal Sets, GQ 6.2	HW 6.2, IQ 6.2
		6.3 Orthogonal Projections, GQ 6.3	HW 6.3, IQ 6.3
27	Tu 04/04	6.4 The Gram-Schmidt Process
		7.1 Diagonalization of Symmetric Matrices, GQ 7.1	Post-assessessment
28	Th 05/06	Review, GQ 4.0, GQ 5.0
	TBA	Common Final Exam (Chapters 1 through 6) in room TBA	Note the date, time, room!