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.