Pay me back multiples.

So non negative multiples of 3.

Can I split myself up into multiples?

We could just look at the multiples.

So let's write all the multiples of 10.

It's equal to multiples of these two vectors.

The scalar multiples, obviously, are any real number.

And I want to see what those multiples are.

The other ones are some multiples of that length.

Let me just mark only the multiples of 9.

Those are literally the nearest multiples of ten that

Our first coordinate is going to be multiples of v1.

We could pick one of these guys and keep taking their multiples, and then figuring out whether those multiples are both divisible by 5 and 15.

Let's see if we can identify what the common multiples are.

If they're collinear and kind of the scalar multiples the same.

And so anything that you were able to generate with V2 before, you can now generate with our U1, multiples of that, plus multiples of our new vector.

And you'll see over here, these are multiples of the number 27.

This is v1 or this is v1, so it's multiples of v1.

And then I could do all the multiples of v1 like this.

European Expansion or Putin Expansion?

But out of the ones we listed 40 and 80 are our common multiples.

Or they could be negative multiples, so they could also go in that direction.

Where you're starting at the origin right there, plus multiples of these two guys.

All of the possible scalar multiples of v are going to be the same thing as all of the scalar multiples of our unit vector, u, which is just a scalar multiple of v.

Multiples of 8 are 8, 16, 24, 32, 40, 48, 64, 72, 80 and so on.

Mission expansion

Mission expansion

Expansion algorithm

Expansion ROM

Expansion Filter

(last expansion

So you take all the multiples of v1, you're going to get every point along this line.

Let's say that, of your free variables, your free variables are going to be the scalar multiples.

So I could draw another version of v2, just like that, just all the multiples of v2.

So let's write these in terms of multiples of 3, since we know that that's the increment level.

Increase expansion level

Decrease expansion level

Protected Areas (expansion)

Protected areas (expansion)

It only has an i component, or all of its vectors are only multiples of the i unit vector.

And it keeps going, because obviously, you could get negative multiples of my vector, and it also goes here.

Simply applying the current market multiple ignores the possibility that current multiples may be high or low by historical standards.

Expansion of strategic partnerships

(Mission expansion and elections)

Expansion of financial services.