# Matrices and Vectors

I’ve been asked by some curriculum writers to offer my thoughts on how I might introduced MATRICES and VECTORS to high-school students in response to the Common Core State Standards N-VM. In response I have done two things:

i) Written a 69-page chapter on introducing these concepts (TOC below.)
ii) Quickly put together some very rough overview videos of my approach.

Here is the series of rough overview videos:

And here is the ToC of what you are in for if you want to look at my sequence of thoughts and suggestions (Feel free to write to me to comment on what you think of all this!)

The Common Core State Standards ……………………………… 2

PART I: MATRICES
Theme 1: Networks ……………………………… 6
Theme 2: Systems of Linear Equations ……………………………… 13
Theme 3: Complex Numbers and Transformations……………………………… 26

Collecting Thoughts and an Epiphany ……………………………… 28
The Confused Role of Technology ……………………………… 33
Do Inverse Matrices Exist? ……………………………… 34

Required Extra Material
Is Every Transformation of the Plane given by a Matrix? ………… 38
The Geometric Interpretation of Determinant……………………………… 40
The “Arithmetic” of Square Matrices ……………………………… 43

PART II: VECTORS
What is a vector ? ……………………………… 48
Vectors between points ……………………………… 51
Vectors and Geometry ……………………………… 54
The Equation of a Line ……………………………… 58
Fun Applications ……………………………… 60