There it comes, these zeroes after zeroes after zeroes.

584, three zeroes.

I'm just arbitrarily stopping the zeroes.

You'd have n minus 1 zeroes plus 0 and you'd have an a2 and then you'd have a bunch of zeroes.

We only want zeroes after the hundreds place.

We're trying to find the zeroes of this...

It's going to be a bunch of zeroes.

So that's 13 zeroes and then a 1.

A decimal, then 13 zeroes and a 1.

One million is one followed by six zeroes.

We have our three zeroes at the end.

It's 0, lambda 2, and then a bunch of zeroes.

You have nine zeroes and then you have this 3.

There's going to be zeroes there when you shift it.

It's just going to be 101 with two zeroes, right?

And so if they didn't tell us 462, we would just put three zeroes here, and that would also fulfill the six zeroes we need behind 645,000,000.

Lambda 1, and then we just have a bunch of zeroes.

This is a 6 with 14 zeroes a very large number.

It is one, two, three, four, five, six, seven, eight, nine zeroes.

This is equal to 645, and then we have our six zeroes.

This will look like a1 and then you'd have a bunch of zeroes.

Well, 11 times 3 is 33, and then we have two zeroes here.

So we still have a remainder, so let's keep bringing down some zeroes.

It's like you can view these as ones and zeroes in some type of computer language, but really they're not just ones and zeroes, because they can take on four different values.

Well, it's going to be 584 with three zeroes behind it, or you could view it as 584 times the 1, and then you're going to have three zeroes in the final answer.

And our nth column is lambda n with just a bunch of zeroes everywhere.

So it's going to be zeroes all the way down to the nth term.

And then it goes zeroes all the way down. And you keep doing this.

You can keep adding as many zeroes as you need until you're done dividing.

Now, I said it'll become a little bit of second nature to you in a little bit, and the way to think about that, the easiest way to think about that, is millions will have six zeroes behind them, thousands will have three zeroes behind them, and just regular numbers have no zeroes behind them.

So you're going to have one, two, three, four, five, six, seven, eight, nine zeroes.

You want to have all the decimals there, so let's put some zeroes out here.

And depending on what dimension we're in, it just means a vector with all zeroes.

So it's going to be equal to lambda 1, and then there's a bunch of zeroes.

But let's figure out what it ends up being, so let's throw some zeroes out there.

12 times 3 is 36, and then we have these two zeroes, so it's equal to 3,600.

So you have 3 times 4 is 12, which we know, and then we have two zeroes.

It's 1,000 times 1,001 over 2, which is equal to well, we'll just add three zeroes to this

So as soon it has been to the sea, it changes the pattern of zeroes and ones here.

And, just a little terminology, these are also called the zeroes, or the roots, of f of x.

30 times 40 is the same thing as 3 times 4 with two zeroes, so let's do that.

Then we're going to have a bunch of zeroes equaling some number, which tells us that there's no solution.

So if you go all the way to the nth column or the nth column vector, you have a bunch of zeroes until you get you have n minus 1 zeroes, and then the very last component, the nth component there will be a 1.

1, 0, 0, and then I have the entry 1, 2, and then I have a bunch of zeroes over here.

These zeroes are just kind of telling you are just shifting it based on the units of measurement that you're using.