## Course coordinator

Eli Stines

ejstines@iastate.edu

515-294-6405

## Catalog description

**MATH 2070: 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 2070 and MATH 3170 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