# Math 207 - Matrices and Linear Algebra

## Course Coordinator

Eli Stines (ejstines@iastate.edu)

## Catalog Description

MATH 207. Matrices and Linear Algebra.
(3-0) Cr. 3. F.S.SS. Prereq: 2 semesters of calculus
Systems of linear equations, determinants, vector spaces, linear transformations, orthogonality, least-squares methods, eigenvalues and eigenvectors. Emphasis on methods and techniques. Only one of MATH 207 and MATH 317 may be counted toward graduation.

## Textbook Lay
Linear Algebra, 5th Edition
ISBN: 978-0321982384

## Syllabus

Chapter and Section references are to Lay, Linear Algebra 5th ed.

Times are suggested based on a 15-week semester of 44 class meetings, allowing for three unit exams, and two weeks worth of classes for review and exams.

Chapter & Sections Topics Weeks
Chapters 1 and 2 5
Sec 1.1-1.9, 2.1-2.6
Chapters 3 and 4
3
Sec 3.1-3.3, 4.1-4.7
Chapters 5 and 6
4
Sec 5.1-5.5, 6.1-6.6
Chapter 7
1
Sec 7.1, 7.2, 7.4

## Objectives

Systems of Linear Equations

• Recognize and set up a system of linear equations
• Perform row operations on a system of linear equations to obtain echelon and reduced echelon forms
• Interpret echelon forms to determine solution sets of systems of linear equations
• Apply systems of linear equations to problems in networking, balancing chemical equations, and other areas

Matrix Algebra and Determinants

• Perform matrix arithmetic operations
• Use determinants do determine if a matrix is invertible
• Use determinants to find the inverse of a matrix if it exists
• Apply augmented matrices to find the inverse of a matrix if it exists

Vector Spaces

• Identify subspaces of n-dimensional real space
• Identify subspaces of abstract vector spaces
• Produce a basis for a given vector space
• Verify if a given set is linearly independent, spanning, or both
• Identity the standard subspaces NulA, ColA, and RowA for a given matrix A

Linear Transformations

• Give the standard matrix for a given linear transformation
• Interpret matrix multiplication as a composition of linear transformations
• Find change of base matrices and their relationship to a linear transformation
• Relate one-to-one and onto with NulA and ColA and invertibility

Eigenvalues and Eigenvectors

• Understand the definition of eigenvalues and eigenvectors
• Verify if given scalars are eigenvalues
• Use the characteristic polynomial to find all eigenvalues and eigenvectors
• Use the number of eigenvectors to determine if a matrix is diagonalizable

Inner Product Spaces

• Understand orthogonality and magnitude in n-dimensional space
• Utilize inner products in abstract vector spaces
• Use an inner product to induce a norm
• Understand the Gram-Schmidt orthonormalization algorithm, and its relation to the QR-factorization
• Utilize matrices to solve least squares problems

(none available)

## Official Math Department Policies

The Math Department Class Policies page describes the official policies that all instructors have to follow. It covers rules on make-up exams, cheating, student behavior, etc.

## Students With Disabilities

If you have a documented disability and require accommodations, you should obtain a Student Academic Accommodation Request (SAAR) from the Disability Resources office (Student Services Building, Room 1076, 294-6624 or TDD 294-6335, disabilityresources@iastate.edu or accommodations@iastate.edu). Please contact your instructor early in the semester so that your learning needs may be appropriately met.