Change of Basis Theorem (Part 1)

First part of a lecture on the change of basis theorem in linear algebra. Here I define coordinates coming from a basis, and the matrix of a linear transformation in a basis, and show how everything can be interpreted as a linear transformation.

[TheBigBangggggg]

I think this is a "strange" way of teaching the subject. When you start with a simple example and then generalize it, I think students will better understand it and in MUCH less time.