LIST OF TOPICS
The following is a list of topics that will be covered in this course along with the chapter and section numbers. The chapter and section numbers are taken from the textbook "Linear Algebra" (3rd Edition), by J. Fraleigh and R. Beauregard. There may also be several concepts presented that are not in the book.

CHAPTER 1. VECTORS, MATRICES, AND LINEAR SYSTEMS

1.1 Vectors in Euclidean Spaces
1.2 The Norm and the Dot Product
1.3 Matrices amd their Algebra
1.4 Solving Systems of Linear Equations
1.5 Inverses of Square Matrices
1.6 Homogeneous Systems, Subspaces, and Bases

CHAPTER 2. DIMENSION, RANK, AND LINEAR TRANSFORMATIONS

2.1 Independence and Dimension
2.2 The Rank of a Matrix
2.3 Linear Transformations of Euclidean Spaces
2.4 Linear Transformations of the Plane

CHAPTER 3. VECTOR SPACES

3.1 Vector Spaces
3.2 Basic Concepts of Vector Spaces

CHAPTER 4. DETERMINANTS

4.1 Areas, Volumes, and Cross Products
4.2 The Determinant of a Square Matrix
4.3 Computation of Determinants and Cramer's Rule

CHAPTER 5. EIGENVALUES AND EIGENVECTORS

5.1 Eigenvalues and Eigenvectors
5.2 Diagonalization
5.3 Two Applications

CHAPTER 6. ORTHOGONALITY

6.1 Projections
6.2 The Gram-Schmidt Process
6.3 Orthogonal Matrices
6.4 The Projection Matrix