Module 1:
Linear Systems and Matrices

Includes:

• Introduction to Linear Systems

• Solving Linear Systems

• Homogeneous Systems

• Basic Matrix Operations

• The Matrix Inverse

• Linear Combinations

• Parametric Vector Form

• Partitioned Matrices

• LU Decomposition

• Linear and Matrix Transformations

Module 2:
Determinants and Vector Spaces

Includes:

• Basics of the Determinant

• Determinants and Operations

• More on Determinants

• Vector Spaces and Subspaces

• Basis and Dimension

• Column, Row, and Null Space

• Coordinate Vectors

Module 3:
Eigenvalues and Inner Products

Includes:

• Eigenvalues and Eigenvectors

• Diagonalization

• Dot Product

• Orthogonality

• The Gram-Schmidt Process

• Least Squares

• Inner Product Spaces