Simon Fraser University
Engaging the World

Course Outlines

Summer 2025 - MATH 240 D200

Algebra I: Linear Algebra (3)

Class Number: 4896

Delivery Method: In Person

Overview

  • Course Times + Location:

    May 12 – Aug 8, 2025: Mon, Wed, Fri, 11:30 a.m.–12:20 p.m.
    Burnaby

  • Prerequisites:

    MATH 150 or 151 or MACM 101, with a minimum grade of C-; or MATH 154 or 157, both with a grade of at least B.

Description

CALENDAR DESCRIPTION:

Linear equations, matrices, determinants. Real and abstract vector spaces, subspaces and linear transformations; basis and change of basis. Complex numbers. Eigenvalues and eigenvectors; diagonalization. Inner products and orthogonality; least squares problems. Applications. Subject is presented with an abstract emphasis and includes proofs of the basic theorems. Students with credit for MATH 232 cannot take this course for further credit. Quantitative.

COURSE DETAILS:

Linear Equations

  • Systems of Linear Equations, Row Reduction and Echelon Form
  • Vectors, Vector Equations, Matrices
  • The Matrix Equation Ax=b
  • Solution Sets of Linear Systems
  • Matrix Inverse
  • Linear Independence, Rank and Dimension
  • Introduction to Linear Transformations
  • The Matrix of a Linear Transformation
Vector Spaces
  • Vector Spaces and Subspaces
  • Null Spaces, Column Spaces, and Linear Transformations
  • Linearly Independent Sets; Bases for Subspaces
  • Coordinate Systems
  • The Dimension of a Vector Space
  • Change of Basis
Determinants
  • Determinants and their Properties
  • Cramer's Rule
Complex Numbers
  • Arithmetic in Cartesian Co-ordinates
  • The Complex Plane,Complex Conjugate, and Magnitude
  • Polar Form, De Moivre's Formula and Euler's Formula
  • Roots of Quadratic Polynomials
Eigenvalues and Eigenvectors
  • Complex Eigenvalues
  • The Characteristic Equation
  • Diagonalization
  • Eigenvectors and Linear Transformations
  • Application: The Leslie Age Distribution model
Orthogonality and Least Squares
  • Inner Product, Length and Orthogonality
  • Orthogonal Sets
  • Orthogonal Projections
  • The Gram-Schmidt Process
  • Application: Least Squares Problems

Grading

  • Homework / Quizzes 10%
  • Hand-In Proofs 10%
  • Midterm 1 15%
  • Midterm 2 15%
  • Final Exam 50%

Materials

REQUIRED READING:

Linear Algebra and Its Applications
6/E
DAVID C. LAY; JUDI J. MCDONALD; STEVEN R. LAY
Pearson Education
ISBN: 9780135851159

REQUIRED READING NOTES:

Your personalized Course Material list, including digital and physical textbooks, are available through the SFU Bookstore website by simply entering your Computing ID at: shop.sfu.ca/course-materials/my-personalized-course-materials.

Registrar Notes:

ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS

At SFU, you are expected to act honestly and responsibly in all your academic work. Cheating, plagiarism, or any other form of academic dishonesty harms your own learning, undermines the efforts of your classmates who pursue their studies honestly, and goes against the core values of the university.

To learn more about the academic disciplinary process and relevant academic supports, visit: 


RELIGIOUS ACCOMMODATION

Students with a faith background who may need accommodations during the term are encouraged to assess their needs as soon as possible and review the Multifaith religious accommodations website. The page outlines ways they begin working toward an accommodation and ensure solutions can be reached in a timely fashion.