# Math 207 – Matrices and Linear Algebra

## Course coordinator

Eli Stines
ejstines@iastate.edu
515-294-6405

## 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 applications and techniques. Only one of MATH 207 and MATH 317 may be counted toward graduation.

## Textbook

Linear Algebra, 6th Edition
Lay
ISBN: 9780136880929

## 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 1 and 2 (5 weeks)
• Sec 1.1-1.9 and 2.1-2.6
• Chapter 3 and 4 (3 weeks)
• Sec 3.1-3.3 and 4.1-4.7
• Chapter 5 and 6 (4 weeks)
• Sec 5.1-5.5 and 6.1-6.6
• Chapter 7 (1 week)
• Sec 7.1 and 7.2 and 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

## Free expression statement

Iowa State University supports and upholds the First Amendment protection of freedom of speech and the principle of academic freedom in order to foster a learning environment where open inquiry and the vigorous debate of a diversity of ideas are encouraged. Students will not be penalized for the content or viewpoints of their speech as long as student expression in a class context is germane to the subject matter of the class and conveyed in an appropriate manner.

## Students with disabilities

Iowa State University is committed to assuring that all educational activities are free from discrimination and harassment based on disability status. Students requesting accommodations for a documented disability are required to work directly with staff in Student Accessibility Services (SAS) to establish eligibility and learn about related processes before accommodations will be identified. After eligibility is established, SAS staff will create and issue a Notification Letter for each course listing approved reasonable accommodations. This document will be made available to the student and instructor either electronically or in hard-copy every semester. Students and instructors are encouraged to review contents of the Notification Letters as early in the semester as possible to identify a specific, timely plan to deliver/receive the indicated accommodations. Reasonable accommodations are not retroactive in nature and are not intended to be an unfair advantage. Additional information or assistance is available online at www.sas.dso.iastate.edu, by contacting SAS staff by email at accessibility@iastate.edu, or by calling 515-294-7220. Student Accessibility Services is a unit in the Dean of Students Office located at 1076 Student Services Building.