### Motivation

When I was learning Linear Algebra in University, I found it was hard to understand what would applications of this course. I remember that we learned determinant on Chapter 1, then we learned a lot of other concept such as Rank and EigenValue. I could only memorize one after another theorems without knowing why these happened to appear this way. However, when I was learning matrices from lectures taught by **Gilbert Strang**, I found every conclusion is so nature that I could easily understand and associate a bunch of concepts with each other. I’d like to conclude what I had learned from him as well as hoping that someone can learn from that.