Multiplication is awesome! Won’t it be great if every matrix was diagonal.
Elementary matices are the matrices that correpond to elementary row operations. Figure them out with class. It’ll be fun.
They are a thing. You feel great them you get it to work.
We can think of AB as B acting on A or as A acting on B. We can demonstrate this with diagonal matrices. here it is.
What does invertible mean?
When is a linear transform T invertible?
What are some obvious transform that are not invertible?
What are some obvious transform that are invertible?
What are some obvious inverses we can figure out?
How can we compute this inverse?