# MATH 362 Syllabus

### Linear Algebra I

Revised: February 2015

## Course Description

Systems of equations, matrices, vector spaces, and linear transformations. Prerequisites: MATH 153, and MATH 250. Three semester hours.

## Student Learning Objectives

By the end of the course students should be able to

• Demonstrate their knowledge of the use of matrices in solving systems of linear equations;
• Use, explain, and verify properties of vector spaces and subspaces;
• Explain and make use of linear independence of vectors, particularly with respect to columns or rows of matrices;
• Explain the meaning and significance of linear transformations;
• Identify eigenvalues and eigenvectors of matrices and interpret their significance;
• Identify innate connections/relations between key topics (properties, theorems, and definitions) from the semester;
• Demonstrate analytical skills in proving theorems and corollaries of linear algebra;
• Apply theorems to solve problems; and
• Master algorithmic aspects of linear algebra.

## Text

L.E. Spence, A.J. Insel, and S.H. Friedberg, Elementary Linear Algebra: A Matrix Approach, 2nd Edition. Pearson/Prentice Hall (publishers) 2008.

Grading procedures and factors influencing course grade are left to the discretion of individual instructors, subject to general university policy.

## Attendance Policy

Attendance policy is left to the discretion of individual instructors, subject to general university policy.

## Course Outline

• Chapter 1: Matrices, Vectors, and Systems of Linear Equations (11 days)
Sections 1 - 4, 6 & 7, with selected applications in section 5 as time allows. Matrix operations and their properties, Linear combinations, Systems of linear equations, Gaussian elimination, Span of a set of vectors, Linear independence and dependence, and selected applications (time allowing)
Note: Inclusion of Gaussian elimination (Section 9.1) is also appropriate at this time.
• Chapter 2: Matrices and Linear Transformations (10 days)
Sections 1, 3,4,7 and 8, with selected applications from sections 2, 5 and 6 as time allows. Matrix multiplication, Matrix inverses, Elementary matrices, Linear transformations of matrices, and applications (as time allows)
• Chapter 3: Determinants (3 days)
Sections 1 and 2. Introduction to determinants, Cofactor expansion, and Properties of determinants.
• Chapter 4: Subspaces and Their Properties (8 days)
Sections 1-5; Subspaces, Basis and dimension, Coordinate systems, and Matrix representation of linear operators. Note: Material from Chapter 7 can be incorporated with this discussion, as desired.
• Chapter 7: Vector Spaces (3 days added to Chapter 4 material )
Sections 1-4 General vector spaces, Subspaces, Linear transformation, Basis and dimension, and Matrix representation of linear operators.
• Chapter 5: Eigenvalues, Eigenvectors, and Diagonalization (4 days)
Section 1, with optional coverage of other sections (section 3 recommended if time allows) Eigenvalues and eigenvectors. Diagonalization of matrices and/or other applications as time allows.