# Fall 2022 - MATH 240 D100

## Overview

• #### Course Times + Location:

Sep 7 – Dec 6, 2022: Mon, Wed, Fri, 11:30 a.m.–12:20 p.m.
Burnaby

• #### Exam Times + Location:

Dec 17, 2022
Sat, 3:30–6:30 p.m.
Burnaby

• #### Instructor:

Jake Levinson
jlevinso@sfu.ca
1 778 782-4853
• #### 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
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

• Quizzes 10%
• Midterm 1 20%
• Midterm 2 20%
• Final Exam 50%

#### NOTES:

THE INSTRUCTOR RESERVES THE RIGHT TO CHANGE ANY OF THE ABOVE INFORMATION.
Students should be aware that they have certain rights to confidentiality concerning the return of course papers and the posting ofmarks.
Please pay careful attention to the options discussed in class at the beginning of the semester.

#### REQUIREMENTS:

This course is delivered in person, on campus, and students are expected to attend all lectures. Should public health guidelines recommend limits on in person gatherings, this course may include virtual meetings. As such, all students are recommended to have access to strong and reliable internet, the ability to scan documents (a phone app is acceptable) and access to a webcam and microphone (embedded in a computer is sufficient).

## Materials

Linear Algebra with Applications
W. Keith Nicholson

This is an open textbook freely available on the following webpage:
https://lyryx.com/linear-algebra-applications/