This book is designed to deal with all of the concepts of linear algebra first in R2, a simple context where algorithmic concerns are minimized and geometric intuition can be brought to bear. Then those same concepts are dealt with in full generality. I find that this conceptual front loading helps in the understanding of the rest of the material. Students can see easily what aspects of the plane are focused on when we think of it as a vector space; linear transformations can be understood as deformations of the plane of a very special type. Nothing more complicated than the solution of quadratic equations or the solution of systems of equations in two unknowns is needed-background which can be quickly resurrected from high school algebra.
Each section of the book introduces some concepts with a variety of examples. The exercises include straightforward computations, quick corollaries of theorems, proofs of parts of major theorems, and (in many sections) applications or further theoretical developments in the form of Project Problems. Answers to the odd numbered problems are included in the appendix, and there is a complete solutions manual available to instructors.
The solutions manual will only be given to credentialed instructors. To obtain a copy, contact Stacy Tichenor in the IWU Math Department at firstname.lastname@example.org.
Stout, Lawrence, "Linear Algebra" (2011). Scholarship. 86.