You also have a rotation matrix that will rotate the model or anything else around the y axis.

This just means my

And so on this slide, you know this matrix is the matrix A, and this matrix is the matrix A inverse.

So for each predictor, we're gonna have one beta or one regression coefficient.

I got a 2 by 2 matrix.

We have the peg legs there, that are all handmade and fitted to you.

Matrix

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learned from Wikipedia, the correct term is the adjugate of matrix a.

I think you see the pattern.

So the inverse of matrix a is equal to 1 over the determinant of a times the adjugate, or adjoint, of matrix a.

So the matrix A is a m by n dimensional matrix, so m rows and n columns and we are going to multiply that by a n by 1 matrix, in other words an n dimensional vector.

So A is a three by two matrix and features

Could I have multiplied the matrices the other way?

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So let me write that down.

It's going to be 2, 1, 1, 1.

It's just a little tedious.

It's the determinant.

So there you have it.

We are almost done.

So B inverse is going to be equal to 1 over the determinant of B.

The inverse is shown like this a negative 1 in the superscript.

Let's calculate B inverse.

We go back to plus.

Matrix

matrix

Let me just quickly show you an example.

In order to get, what

By train?

What's the line for?

Just to say that again.

If you solve the problem, you have probably something like this.

And actually this step is fairly straightforward.

So, just to wrap up the terminology, matrix that don't have an inverse Sometimes called a singular matrix or degenerate matrix and so this matrix over here is an example zero zero zero matrix. is an example of a matrix that is singular, or a matrix that is degenerate.

Now we're doing it in matrix form.

Modelling transforms.

First matrix

First let's put the data into octave.

What is this thing right here?

And if you do that, the result is pretty much what you'll expect.

You can also take a matrix and divide it by a number.

I am going to construct a matrix as follows.

So, a matrix is

Last one.