I hear it operating. I probably smell it operating. (Laughter)

The phone is working.

And the definition of our linear transformation, or the composition of our linear transformation.

The television doesn't work.

But does it work?

Independence.

linear regression.

The air conditioner was on.

But, but it didn't work.

This is how most work today.

Use linear mode

Linear middle of the distribution

It's a linear combination of the columns.

Tom works for an oil company.

It also runs on the iPhone.

And so that's how this all operates.

Tom worked for an oil company.

Sami's television was still on.

I see the memory operating, I see the CPU operating,

Now, I have this device on.

And all a linear combination of vectors are, they're just a

do the linear combinations of the columns fill three dimensional space?

Right? Because that's not the way the world works.

Some engineer! He should've been a grave digger!

learned linear algebra.

planes, because they're not parallel, they're not special.

So we would be having the linear combinations of nine vectors in

And then I have a final linear transformation f.

And I call it linear change. Unlike cyclical change, when linear change hits we're not going back.

The notion that you can understand why a brain works, perhaps.

And so this works the same way you pick it up and pop it open.

And this whole book, it doesn't just run on the iPad.

We don't know how it works.

A linear transformation of x, of our vector x, is the same thing as taking the linear transformation of this whole thing let me do it in another color is equal to the linear transformation of actually, instead of using L,

MV is the linear middle of the distribution.

And that's what's neat about algebra.

There's a lot of names and labels in linear algebra.

Let me show you a concrete example of linear combinations.

linear algebra, and I'm Gilbert Strang.

Let's say I have the linear transformation g.

When it's built, you'll finally be able to understand how a computer works, because rather than having a tiny chip in front of you, you've got to look at this humongous thing and say, Ah, I see the memory operating, I see the CPU operating, I hear it operating. I probably smell it operating.

Sami worked occasionally as a handyman.

So it runs frequently, the entire hospital, just on a generator.

Can never tell if it's on.

It's actually running at real rate right now, one second per second, and in fact,