Syllabus and Course Information, Fall 2023
MATH 225 SL1 at TR 3:00pm-3:50pm in 1WOHLR 141
1. Textbook: Linear Algebra and its Applications, 6thedition by David C. Lay,
Stephen R. Lay, and Judi J. McDonald, Addison-Wesley
Some course material including an online version of the text will be available from a
Pearson MyLab website for which you need the following login information:
Course Name: MATH 225 Fall 2023
Course ID: bradlow43862
2. Syllabus:
Chapter 1: Linear Equations in Linear Algebra
1.1 Systems of Linear Equations
1.2 Row Reduction and Echelon Forms
1.3 Vector Equations
1.4 The Matrix Equation Ax=b
1.5 Solution Sets of Linear Systems
1.6 Applications
1.7 Linear Independence
Chapter 2: Matrix Algebra
2.1 Matrix Operations
2.2 The Inverse of a Matrix
2.3 Characterizations of Invertible Matrices
2.6 The Leontief Input-Output Model
Chapter 3: Determinants
3.1 Introduction to Determinants
3.2 Properties of Determinants
3.3 Cramer's Rule, Volume, and Linear Transformations
Chapter 4: Vector Spaces
4.1 Vector Spaces and Subspaces
4.2 Null spaces, Column Spaces, and Linear Transformations
4.3 Linearly Independent Sets: Bases
4.5 The Dimension of a Vector Space
4.6 Change of basis
Chapter 5: Eigenvalues and Eigenvectors
5.1 Eigenvalues and Eigenvectors
5.2 The Characteristic Equation
5.3 Diagonalization
Chapter 6: Orthogonality and Least Squares
6.1 Inner Product, Length, and Orthogonality
