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

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

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

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

I think you see the pattern.

This just means my

It's the determinant.

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

We go back to plus.

It's just a little tedious.

We are almost done.

In order to get, what

What's the line for?

Just to say that again.

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

I got a 2 by 2 matrix.

Let's calculate B inverse.

Matrix

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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.

Now we're doing it in matrix form.

Modelling transforms.

First matrix

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.

You have plus, and then you go minus.

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

And actually this step is fairly straightforward.

So it turns out that we can multiply two matrices.

That's the first column, that's the second column, that's the third column So, this second matrix we say it is a 2 by 3 matrix.

This is good as this is another example so I'm going to multiply this matrix

Otherwise, we just move onto the next entry.

Well you cross out row 1, column 3.

So the area of your parallelogram squared is equal to the determinant of the matrix whose column vectors construct that parallelogram.

Could I have multiplied the matrices the other way?

Finally, the last special matrix operation I want to tell you about is to do matrix transpose.

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So let me write that down.

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

Function MMULT multiplies two matrices. Number of columns of the first matrix must be the same as row count of the second one. The result is a matrix.

And then, remember that to do matrix multiplication, the two matrices have to be conformable.

We ended up with fractions here and things.