1.3 Three-dimensional Euclidean
Building the student's ability to think in more than two dimensions and to link ideas
about lines and planes with inner product. Very useful later for linear independence,
solution sets, subspaces.
2.6 Electric circuits
A nice application of $n$ linear equations in $n$ unknowns. Physical intuition leads us to
expect a unique solution in this particular situation, and it is confirmed.
3.3 Subspaces of R^n
Crucial reinforcement of the concept of subspace with specific examples. Students will
feel they understand a subspace, when they can take a given one and construct a basis.
4.6 Change of basis
How to explain change of basis without introducing any new notation at all. It is a simple
topic, despite the treatment you find in some books!
Exercises for Chapter 5
The exercises are collected at the end of each chapter. It makes the text easier to
review. There is plenty for the instructor to choose from. I tried to stimulate the
7.4 Orthogonal diagonalization
You can do this without knowing what a complex number is. I tried to make this feel very
down-to-earth. You do need to differentiate sine and cosine.
8.8 Linear differential
How to make Jordan form seem worthwhile to students.