Or if I wanted to rewrite that, I could just write that as, the magnitude of the displacement times the magnitude of the force times the cosine of theta.

And this will give me a 3 by 1.

All of my features and organize them efficiently into sort of one big block of numbers like that.

Minus 1 plus 2 is equal to 1.

Further down, you start getting into pre algebra and early algebra.

Further down, you start getting into pre algebra and early algebra.

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

But I'm going to be very formal and very abstract and very broad with the vector right now because the beauty of linear algebra is that it doesn't just apply to things

If I want to assign this to a column vector, what I would do instead is do v 1 2 3.

A Computer Algebra System

Maxima Algebra System

In contrast, using a good numerical linear algebra library in

Let me define a set, s, and it's equal to all of the vectors I can create, if I were to multiply v times some constant, so I multiply some constant, some scalar, times my vector v, and just to maybe be a little bit formal, I'll say such that c is a member of the real numbers.

Ancient Greek Numbers

What I wanna do in this video is think about the origins of Algebra, the origins of Algebra.

Let me define a set I, maybe l for line, that's equal to the set of all of vectors where the vector x, I could do it bold or I'll just draw an arrow on it, plus some scalar I could use c, but let me use t, because I'm going to call this a parametrization of the line so plus some scalar, t times my vector v such that t could be any member of the real numbers.

It's a function of x and y, and it's equal to some scalar function of x and y times the i unit vector, or the horizontal unit vector, plus some other function, scalar function of x and y, times the vertical unit vector.

My a vector looked like that.

In fact, I'd like you to modify this code a little bit more in a way that we have multiple measurements.

I'm saying that theta gets, you know, updated as that's the vector, our N 1.

But I'm going to define my vector.

You really don't understand what you're doing and it really comes out of a little bit of algebra.

So let's see if we can simplify this a little bit.

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

I don't know. I failed algebra.

So. In the next set of videos what I'm going to do is do a quick review of linear algebra.

Vector

vector

But either of those vectors.

Construct the vector difference of the other vector and this one.

Algebra is a branch of mathematics.

The obvious question that you're probably asking is, hey

And that's another equivalent way of assigning A to be the values of this three by two matrix.

Construct the vector sum of this vector and another one.

An interface to the Maxima Computer Algebra System

Let's go to something else.

Now, let's see what we can do.

It's an ancient number system Hang Zhou.

Numbers written in an ancient Chinese dialect.

Let's say it moves in a path that moves something like this.

Algebra is a branch of mathematics.

And, and I agree with you right now.

We're just going to have to break out some algebra or let s can do here.

Construct the vector sum of two vectors.

UV vectors