If you distribute the negative 3, you're going to get that expression.

We're multiplying our f of t times e to the 1t.

The probability, and I will just write a little bit more generally here.

And so, if we just put this on the other side of the equation, what do we get?

You already understand that negative 7 times some number is always going to be negative 7 times that number.

If you want, you can just multiply this guy out and you'll get that right there.

They say, you have found more than one solution that satisfies the system.

That's what multiplying times 10 to the negative 8 did for us.

So you're going to get some combination of the i and j unit vectors.

And then when I multiplied this guy times that guy, what happens?

This seems to be the more logic of point in relative to the mean and the variance of this Gaussian. This point corresponds pretty much to this point over here.

Transform of any arbitrary function very, very quickly.

Because if I introduced any products with any x terms, you're going to get one of these other terms over here.

This we know as 'factorization.'

This 7 times x plus the minus 6 times the other x.

Homework is going to be a little different from quizzes, so unlike the quizzes where you get instant feedback for each question, in the homework you'll submit your answers, and you won't see feedback on them until you submit your answers, and after the deadline for the homework, we'll be posting answers and having discussion about the questions.

So now we just solve for x.

To see, as we go through the data, we can maintain the number of data items that we have.

So let's multiply it by 2.

Now if I multiply this whole thing times dy,

If I was right above the plane, if I were to just draw the plane.

But order of operations would tell us to do it anyway.

So you take 21.50 times 10,000 shares gives us a market cap of 215,000

So it will UNlNTELLlGIBLE that point.

Here, if the weather's good, you can get a lovely view.

You can get a nice view from here when the weather is good.

Got it.

If you distribute this negative sign, you get negative b plus a, which is exactly what this is over here.

All I did is I took the c plus di and I multiplied it by this to get this, and multiplied it by this to get this.

0 times 7 is 0.

It is 4.

That's what builds this term when you multiply it out.

This sounds reasonable.

You give me any x, any y, you give any x, y in the x y plane, and these are going to end up with some numbers, right?

If we look ahead, these kind of changes are going to be increasingly possible.

So that's where you get the intuition that it's x minus 2y times x minus 2y.

And then we would say that x is equal to 5 or x is equal to negative 1.

He's got it.

3a to minus 2b, you get this vector right here, and that's exactly what we did when we solved it mathematically.

So this is our dr right here.

Let's be safe and assume 30. You'll get a normal distribution in your distribution of sample means.

like calcium, potassium and magnesium from out of desalination brine.

4 and negative 21 look tantalizing, but when you add them, you get negative 17.

Or another way of writing that is v1 dot v1.

So if I multiply 2 times my vector a minus 2 3 times my vector b, I will get to the vector 2, 2.