Summer 2023 - MATH 240 D100

Algebra I: Linear Algebra (3)

Class Number: 2187

Delivery Method: In Person


  • Course Times + Location:

    May 8 – Aug 4, 2023: Mon, Wed, Fri, 11:30 a.m.–12:20 p.m.

  • Exam Times + Location:

    Aug 9, 2023
    Wed, 12:00–3:00 p.m.

  • Instructor:

    Jonathan Jedwab
    1 778 782-3337
  • 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.



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.


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 and their Properties
Complex Numbers
  • 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


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



Linear Algebra and Its Applications
Lay, Steven R.; Lay, David C.; McDonald, Judith; McDonald, Judi J.
Pearson Education
ISBN: 9780135851043


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