That's one of our bluefin at the Monterey Bay Aquarium.

What you did with the streamlining was fantastic.

One term you are going to hear a lot of in these videos, and in linear algebra in general, is the idea of a linear combination.

learning algorithms, if you're able to take advantage of these

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Now, the next thing you'll see when you start discussing

Walkie Talkie?

So I just showed you, I can find this vector with a linear combination.

This style of hat is now in fashion.

Wires carry electricity.

Beyond drag, lift and stretch there are many other properties we could simulate.

In the autumn of 1917,

In the autumn of 191 7,

That's all a linear combination is.

So the span of the 0 vector is just the 0 vector.

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

These are all just linear combinations.

For instance, here's the trajectory of Marc Chagall, an artist born in 1887.

This type of camera is now out of fashion.

In contrast, using a good numerical linear algebra library in

And I define the vector b to be equal to 0, 3.

6 minus 2 times 3, so minus 6, so it's the vector 3, 0.

When a coil is moved near to a wire with current flowing in it current flows in the coil as well.

And so here I introduce something, the set of rivers of a plane filling curve.

You get this vector right here, 3, 0.

But don't forget, the electricity has to be switched on this time.

The hairstyle has caught on with the girl students.

They're in some dimension of real space, I guess you could call it, but the idea is fairly simple.

A small bridge arched the stream.

She typically buys a cow. The cow gives milk.

That's why it's called a linear function.

If we make it minus 5, what happens?

That tells me that any vector in R2 can be represented by a

So this will be the typical workflow situation.

Here is the preliminary result, which I can show because it's already been shown.

We're dealing with y is equal to x squared, which you should hopefully be reasonably familiar with at this point.

This is just different ways of representing the same information, the same idea.

And this is just one member of that set.

It'll be a vector with the same slope as either a or b, or same inclination, whatever you want to call it.

like maybe not that many edges, like a star graph for example.

About a week later we had a problem with the machine, related actually to these bits of wire here these gold wires.

According to the flyer, at precisely 10 04 p.m. this Saturday night lightning will strike the clock tower, electrifying the cable as the connecting hook makes contact thereby sending 1.21 gigawatts into the flux capacitor and sending you back to 1985.

In contrast, using a good numerical linear algebra library in

Now you might say, hey Sal, why are you even introducing this idea of a linear combination?

So we can fill up any point in R2 with the combinations of a and b.