Folio

Switch knives.

Switchblade knives.

Rolled up or folded?

Folded, I think.

And then within the chloroplast itself, you have these little stacks of these folded membranes, These little folded stacks.

This is a letter of the alphabet that's been folded just once.

The telescope, going up in space, it unfolds in two places.

We collaborated with Oldenburg and put the newspaper on top, folded.

Then upper triangular, everything below the diagonal is a 0, and everything above the diagonal probably isn't a 0, but you never know.

So the transformation of x2 is equal to our transformation matrix 1, 2, minus 1, 0 times 2, minus 2. And so this will be equal to 1 times 2 is 2. Plus minus 1 times minus 2.

Alice looked up, and there stood the Queen in front of them, with her arms folded, frowning like a thunderstorm.

1, 2, minus 1, 0 times minus 2 minus, minus 2. And so what would this be equal to?

This just comes from the definition of a 2 by 2 determinant.

2 minus 2 times 1 is 0.

Right by twos!

I'm ignoring the zero because it's in the same column as the 1, 2, 0 0, 2, 3, and then 2, 0, 0.

1 minus 2 minus so it's 1 minus 2 plus minus 1 times minus 2. That's going to be plus 2.

this is tucked in some small solid, but the moment it evaporates, it's merged with the whole.

And our lander is safely tucked inside what we call an aero shuttle.

And I've really not done anything much more complicated than make foldout pages.

And our lander is safely tucked inside what we call an aeroshell.

We defined the determinant of a 2 by 2 matrix not in terms of a determinant.

0 minus 2 times 1, that's minus 2.

2 minus 2, times 1, is 0.

5 minus 2, times 2, is 1.

Two by two. Right and left.

Let's take our transformation of x2.

So it's 1, 0, 2 0, 1, 2 2, 3, 0, just like that.

She had nothing to read or to look at, and she had folded her thin little black gloved hands in her lap.

But the motivation comes from the exact same place as the 2 by 2 version.

So far we've been able to define the determinant for a 2 by 2 matrix.

And then, 0 minus 2 times 1, so that's minus 2.

0 minus 2 is minus 2.

I came up with this letter. This is a letter of the alphabet that's been folded just once.

And then have 2 times 2 is 4. Plus 0 times minus 2. So it's 4, 4.

In the last video we defined the notion of a determinant of a 2 by 2 matrix.

I've got a 2 by 2 matrix here. Let's say A is equal to a, b, c, d. So I'm going to keep it really general.

So times the determinant of the matrix a2 2, a2 3, a3 2, and then a3 3. Just like that.

Well, you keep doing it, and you're going to get all the way down to a 2 by 2 matrix.

And then 2 times minus 2 is minus 4. Plus 0.

Then minus 2 times get rid of that row, that column 0, 3, 2, 0. And then plus 0 times 0, 2, 2, 0. That's this one right there.

Minus 2 times the determinant. You cross these guys. Cross that row and column out.

0 minus 2 is minus 2.

This is 36 times 2.