MATH2019 programs

Linear Algebra

This course provides an introduction to fundamental concepts in linear algebra, including solving linear systems using Gauss-Jordan elimination and other methods, matrix operations, and linear transformations. Students will explore inverse matrices, image and kernel, basis and dimension, and coordinate representations in vector spaces. The course covers orthonormal bases, the Gram-Schmidt process, QR factorization, determinants, eigenvalues, eigenvectors, and matrix diagonalization. Applications to dynamical systems, including complex eigenvalues, will also be discussed. Through theoretical study and practical exercises, students will develop problem-solving skills essential for various fields.

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ECTS

180

hours in a term

class hours a week

From the Fall 2025-2026 syllabus

What you will learn

•Solve systems of linear equations using Gaussian elimination
•Express systems in matrix form and determine their consistency
•Perform matrix operations and compute matrix inverses
•Understand key properties of matrices
•Develop a strong grasp of vector spaces, linear independence, basis, and dimension

How it is graded

10%

Quizzes

Weeks 3, 5, 10, 12, and 14

10%

Participation

Each week except weeks 7, 8, 15, and 16

40%

Midterm exam

Week 8

40%

Final exam

Week 16

Workload

180 hours in a term, about 12 a week

In-Class Time 56 hIndependent Study 50 hAssignments 50 hExaminations 24 h

Week by week

Books

Linear Algebra with Applications

Otto Bretscher, Fourth Edition

required

Introduction to Linear Algebra

Gilbert Strang, Sixth Edition

recommended

Where it fits

NeedsPrecalculus

UnlocksCalculus 3 Probability and Statistics

Requirements come from syllabi. Check with your advisor.

Rules

Attendance is compulsory; a student missing 25% (16 hours or more) of all instructed hours will fail the course. Students more than 15 minutes late may sit in class but are marked absent.

There is no graded homework; missed quizzes receive zero with no make-ups, and make-up exams are considered only in extreme circumstances with a valid medical certificate. Where special consideration is applied for, assignments must still be completed within five days of the submission date or they will not be marked.