Learning Algebra 2

24th Nov, 2021

Matrix multiplication as composition | Chapter 4

Composition is the product of two matrices.

How to compute the product of two matrices:

These are transformations that must be applied sequentially. From previous lessons, we know that each column in a matrix is the coordinate where î (i hat) and ĵ (j hat) will be after the transformation. So, first we must transform the first column [e, g] of the first matrix M1, to see where î goes.

And then we do the same for the second column [f, h] of the first matrix M1, to see where ĵ will go.

And that gives us our composition!

A few properties of matrix multiplication:

Done. Let's move to the 3D realm.