Syracuse University · Fall 2026

MAT 331 First Course in Linear Algebra

Vectors, matrices, transformations, eigenvalues, and the geometric ideas that connect them.

View semester plan Open Blackboard
SectionsM002 · M003
Meeting times
M002 MWF · 9:30–10:25 a.m. M003 MWF · 10:35–11:30 a.m.
LocationCarnegie 219
InstructorPeixue Wu

Course overview

See the structure behind the symbols.

Linear algebra is the language of systems, dimensions, and transformations. We will move from solving equations to understanding the spaces and maps beneath them.

The course covers linear systems; vectors in Rn; independence and bases; linear transformations; matrices and determinants; eigenvalues and eigenvectors; and geometric aspects of linear algebra.

Prerequisite
MAT 286 or MAT 296
Office
Carnegie 206E
Office hours
Monday, 2–3 p.m.; also by appointment
Email
wpeixue@syr.edu

Learning objectives

By the end of the course, you will be able to…

  1. 01

    Solve and analyze systems of linear equations by row reduction.

  2. 02

    Use vectors, matrix algebra, independence, and the Invertible Matrix Theorem.

  3. 03

    Represent linear transformations by matrices and interpret them geometrically.

  4. 04

    Use subspaces, bases, dimension, rank, and determinants to analyze matrices.

  5. 05

    Find eigenvalues and eigenvectors, test diagonalizability, and construct orthogonal projections.

Assessment

Practice steadily. Show what you know.

Your grade combines routine practice, written reasoning, brief quizzes, and three cumulative checkpoints.

  • WeBWorK10%
  • Written homework10%
  • In-class quizzes10%
  • Midterm Exam 120%
  • Midterm Exam 220%
  • Cumulative final30%

Letter-grade ranges

A
93–100
A−
90–<93
B+
87–<90
B
83–<87
B−
80–<83
C+
77–<80
C
73–<77
C−
70–<73
D
60–<70
F
<60
01

WeBWorK

Short online practice on most sections. Begin early so there is time to ask questions.

Two lowest set scores dropped
02

Written homework

Develop complete arguments and independently write up your work.

Lowest score dropped
03

Quizzes

Brief in-class checks occur during most non-exam weeks.

Lowest score dropped

Semester plan

From row reduction to orthogonal projection.

Midterm dates are tentative until confirmed on Blackboard.

WeekDatesTextTopics and remarks
01Aug. 24–281.1–1.2Linear systems; row reduction; echelon forms
02Aug. 31–Sept. 41.3–1.5Vector equations; Ax = b; solution sets
03Sept. 7–111.7Linear independence No residential classes Sept. 7
04Sept. 14–181.8–1.9Linear transformations and matrix representations
05Sept. 21–25Ch. 1Chapter synthesis, review, and Exam 1 tentative
06Sept. 28–Oct. 22.1–2.3Matrix algebra; inverses; Invertible Matrix Theorem
07Oct. 5–92.8Subspaces; null space and column space
08Oct. 12–162.9Dimension and rank Fall Break Oct. 12–13
09Oct. 19–233.1–3.3Determinants; properties; Cramer's Rule
10Oct. 26–30Chs. 2–3Chapter synthesis, review, and Exam 2 tentative
11Nov. 2–65.1–5.2Eigenvectors, eigenvalues, characteristic equation
12Nov. 9–135.3Diagonalization and its uses
13Nov. 16–206.1–6.2Inner products, length, orthogonality, orthogonal sets
14Nov. 23–27—Thanksgiving Break No residential classes Nov. 22–29
15Nov. 30–Dec. 46.3–6.4Orthogonal projections; Gram–Schmidt process
16Dec. 7ReviewCumulative final review
FinalFri., Dec. 11—Cumulative final exam · two-hour block between 8:00 a.m. and 2:30 p.m.; exact time announced later

Key dates

Plan ahead.

Aug 24

Classes begin

Aug 31

Add deadline

Sept 14

Drop / grading option deadline

Oct 12–13

Fall Break

Nov 20

Withdrawal deadline

Nov 22–29

Thanksgiving Break

Dec 7

Last class day

Dec 11

MAT 331 final exam

Course essentials

Clear expectations, fewer surprises.

Late work

Dropped scores cover ordinary illness, technical trouble, and busy weeks. Late work is ordinarily not accepted; reach out before the deadline about serious circumstances.

Assessments

Unless announced otherwise, assessments are closed-book. Calculators, phones, smartwatches, headphones, and other electronics are not permitted.

Collaboration

Discussing homework ideas is encouraged, but submitted work must be independently written and reflect your understanding.

Artificial intelligence

AI use is limited and assignment-specific. Follow the instructions for each WeBWorK or written assignment; when no permission is stated, AI use is not permitted.

Resources

Everything for MAT 331, in one place.

Announcements and due dates posted on Blackboard are the authoritative course record.

Course hub

Blackboard

Announcements, files, written work, feedback, grades, and the current course schedule.
Practice

WeBWorK

Routine online problem sets. Use the course-specific link posted in Blackboard.

Required text

Linear Algebra and Its Applications

6th edition · David C. Lay, Steven R. Lay, and Judi J. McDonald · ISBN 9780135851258.

Academic support

Drop-In Math Clinic

Drop-in help for MAT 331 in Carnegie 102. The schedule will be posted soon.

Questions?

Ask early. Office hours are part of the course.

Include “MAT 331” in the subject line. I normally respond within two business days.

Email Peixue Wu