Easier do doted line.

So at 5, at y is equal to 5, we will draw a dotted line.

So this green side (I'll draw it as a dotted line), it could be of any length.

If it was a dotted line it would just be less than.

I can draw a straighter than that. I will draw a doted line maybe

let me just draw a little dotted line here so imagine if you were to cut it just like that cut the side of the soda can. and if you were to kind of unwind if you were to unwind this thing that goes around it what would you have?

If they had drawn a dotted line here that means we're not including the line.

Oatmeal tweeds.

Baseline data should be provided where possible for the organizational targets in the results matrix.

Now, I could just graph the line, but because that won't be included in the y's that satisfy this constraint, I'm going to graph it as a dotted line.

Oatmeal tweeds, blouse, blue silk handkerchief. Yes.

And even with global warming if you can see these blue lines, the dotted line shows that even if emissions of greenhouse gasses stopped today, the next decades will see rising sea levels.

5.2.2.2.1.1 Add the following sentence at the end Labels shall be displayed on a background of contrasting colour, or shall have either a dotted or solid outer boundary line. .

5.3.1.1.2 Add the following sentence at the end Placards shall be displayed on a background of contrasting colour, or shall have either a dotted or solid outer boundary line. .

In the deepest snows, the path which I used from the highway to my house, about half a mile long, might have been represented by a meandering dotted line, with wide intervals between the dots.

I'll do it as a dotted line.

I'm told you have a grey Aurelia with blue polkadot upholstery.

So an identity matrix is a matrix.

Let's just do some matrix matrix products.

A 2 by 3 matrix, a 2 by 3 times 3 by 2 matrix, I got a 2 by 2 matrix.

The identity matrix times any other matrix is just that matrix.

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So in general, the nullity of any matrix of any matrix

So it's a 2 by 3 matrix.

Anything times that identity matrix is going to be equal to itself.

It's actually going to be a 3 by 3 matrix, a much bigger matrix.

Cells Array

So, first lets just think about this.

In mathematics, an integer matrix is a matrix whose entries are all integers.

This is equal to some new matrix I'll make it pretty big right here times our vector x .

Or, we would call this matrix, just by convention, you would call this a two by three matrix.

We have a 3 by 2, times a 2 by 3 matrix, so it's going to result in a 3 by 3 matrix.

I get the k by k identity matrix. I get the identity matrix of k, because it's going to be k by n, times n by k.

So that's my original A right there.

OK, so the matrix of cofactors is essentially applying this pattern to the matrix of minors.

Array of tools

I will create an augmented matrix.

It's a diagonal matrix.

Matrix of minors.

To figure out its transformation matrix, so if we say that T of x is equal to, I don't know, let's call it some matrix S times x.

If we have a 2x2 matrix, the identity matrix is 1, 0, 0, 1.

The transformation matrix with respect to that eigenbasis, it becomes a very, very nice matrix.

We multiplied the 3 by 2 matrix times a 2 by 3 matrix, and we got a 3 by 3 matrix.

I could just create a coefficient matrix, where the coefficient matrix would just be, let me write it neatly, the coefficient matrix would just be the coefficients on the left hand side of these linear equations.

Well our change of basis matrix is just the matrix with these guys as the columns.