And then they would tell you that, Hey, look, just from straight up properties of the principal square root function, they'll tell you the square root of a times b is the same thing as the principal square root of a, times the principal square root of b.

So this'll be a because I just distribute the a, right? a times a to the zero, plus a times a to the 1, plus a times a squared, plus all the way a times a to the n minus one, plus a times a to the n.

So, here's a matrix

I've never gotten very good at this.

Now, the big insight you need to have whenever you have an absolute value equation like this is to remember, if I have the absolute value of a is equal to 11 what do we know about a?

So let's do that, and then we'll confirm that it really is the inverse.

So its formula will be y minus y1 is equal to some constant,

Let me just show you what I mean by that.

So if we go from a to the first, which is just a, and divide by a, right, so we're just going to go we're just going to divide it by a.

And it turns out if that you are computing A times A inverse, it turns out if you compute A inverse times

I can't remove this line because we actually need to return A to have the same value.

Well, phi is equal to A over B, which is equal to A plus B over A we know that A plus B over A is the same thing as

Well, if we say that Abby's earnings are represented by a, and Ben's earnings are represented by b, that tells us that a plus b must be 50.

But you should always be able recognize that if you have a minus b over b minus a that that is equal to negative 1.

And it would be extra nice if I could actually switch this multiplication around.

But we already learned that the Laplace transform of sine of a t is equal and we did a very hairy integration by parts problems to show that that is equal to a over s squared plus a squared.

A single click on a file will select and focus, a double click opens the file or steps into the directory.

So what we need to do here, is we need to think of two numbers, a and b, where a times b is equal 4 times negative 21.

Well, if we look at our regular expression, it's also valid that our first character is an a, so this probably means that this transaction is an a.

The probability that J is positive given that A is positive is 0.9.

And a cubed divided by a squared is an a.

Well this is going to be (b) as well.

So you can say a 3 5, then we can say b a a a 1 note means times , it is used for multiplication. and then you can say c a b

So we have this test specifically to check for it.

A is unchanged because there's no rewrite rule in our grammar for dealing with it, but a exp becomes a expression expression, a expression expression, a open expression close, and a num.

And now, according to the first sentence, says that if E or B is true then A is true.

To define NP even more formally, we're going to say a problem is an NP if there is a verification in algorithm.

So, in fact, in general, if you have a matrix operation like

Then we find that the normalizer, P(B), is identical, whether we assume A on the left side or not A on the left side.

It looks something like that.

If you start with the variable a, referring to the list 1, 2, 3, and the variable b, referring to the list 2, 4, 6, then we call union, passing in a and b.

The other thing I want to make clear without the return is that if we passed in variables for this, it still does not change their value.

Same drill.

The next step, you wash your hands in front of a sensor to get liquid soap.

You then run take to take out the sub matrix.

It's a brave thing you're doing.

So can we somehow pattern match this to that?

On the other hand if a is even, then just because of the derivation that we just worked out a moment ago, multiplying a times b is really the same thing as adding b to itself a over 2 times, so it's a over 2 times b, which we're going to compute recursively.

She says property that for any matrix A, A times identity i times A

Well, it's not much.

Thrun And again the solution follows directly from the state diagram over here.

The right hand side, this is asserting, I'm just making a claim that the values of A and B are the same. And so, whereas I can write A A 1, that means increment A by 1.

Think of it as basically the inverse of A and that's the inverse of A and second set, you know, 10 equals p of A and of temp times

And then our denomenator is going to be

If a is greater than c, we know c is the smaller number and a is the median.