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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 Procedure

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)

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.