MATH276

Systems of Linear Equations

Row Reduction and Echelon Forms

Vector Equations

The Matrix Equation, Ax=b

Solution Sets of Linear Systems

Applications of Linear Systems

Linear Independence

Introduction to Linear Transformations

Linear Models in Business, Science, and Engineering

Matrix Operations

The Inverse of a Matrix

Characterizations of Invertible Matrices

Vector Spaces and Subspaces

Null Spaces, Column Spaces, and Linear Transformations

Linearly Independent Sets; Bases

Coordinate Systems

The Dimension of a Vector Space

Rank

Eigenvectors and Eigenvalues

The Characteristic Equation

Diagonalization

Discrete Dynamical Systems

Inner Product, Length, and Orthogonality

Orthogonal Sets

Orthogonal Projections

Least-Squares Problems

Applications to Linear Models in other areas of science.