Teaching
I. Bibliography
Some interesting notes:
http://joshua.smcvt.edu/linearalgebra/book.pdf
http://www.maths.qmul.ac.uk/~pjc/notes/linalg.pdf
https://www.math.ku.edu/~lerner/LAnotes/LAnotes.pdf
and a huge volume:
http://www2.warwick.ac.uk/fac/sci/maths/undergrad/ughandbook/content/ma106/elementary_linear_algebra_10th_edition.pdf
II. Exercise
Vector spaces: Exercises, Ideas.
Trigonalisation: Exercises, Ideas