Linear Algebra - Jim Hefferon - Bog

This text covers a standard first course: Gauss's Method, vector spaces, linear maps and matrices, determinants, and eigenvalues and eigenvectors. In addition, each chapter ends with some brief topics, such as applications.
What sets it apart is careful motivation, many examples, and extensive exercise sets. Together, these help each student master the material of the course and also help an instructor develop that student's level of mathematical maturity.