So it's a set of collinear vectors.

So this R4 means a set of four dimensional vectors.

So what's the set of all of the vectors that I can represent by adding and subtracting these vectors?

This is a set of vectors, and any member of this set is going to look something like this.

The sum or set of all those vectors together form the belief space.

Why am I defining this obtuse set here and making you think in terms of sets and vectors and adding vectors?

And so, our line can be described as a set of vectors, that if you were to plot it in standard position, it would be this set of position vectors.

But either of those vectors.

UV vectors

Vectors Segments

But it begs the question what is the set of all of the vectors I could have created?

Linear algebra gives us a notation and a set of things or a set of operations that we can do with matrices and vectors.

A linear combination of these vectors means you just add up the vectors.

I really, since these are vectors, remember, vectors are special cases of matrices, right?

Invert Normal Vectors

But what is the set of all of the vectors I could've created by taking linear combinations of a and b?

And now the set of all of the combinations, scaled up combinations I can get, that's the span of these vectors.

We just get that from our definition of multiplying vectors times scalars and adding vectors.

Construct the vector difference of two vectors.

Construct the vector sum of two vectors.

And it's composed of two column vectors.

All of these are possible attack vectors.

How can I represent the set of all of these vectors, drawn in standard form, or all of the vectors, that if I were to draw them in standard form, would show this line?

So let me define a couple of vectors.

Select the first of the two possibly equal vectors...

Select the other of the two possibly equal vectors...

So let me define a couple of vectors here.

So I can get to any of these vectors.

Those are my two vectors.

Similarly you can assign vectors.

Vectors give you the result.

R2, by these two vectors.

You've already dealt with vectors.

You can kind of view it as the space of all of the vectors that can be represented by a combination of these vectors right there.

So it's just c times a, all of those vectors.

So if I were to write the span of a set of vectors, v1, v2, all the way to vn, that just means the set of all of the vectors, where I have c1 times v1 plus c2 times v2 all the way to cn let me scroll over all the way to cn vn.

Test whether two vectors are equal

The two vectors are the same.

I have added the two vectors.

So let me pick new vectors.

Often they are 3 dimensional vectors.

Let's say we have two vectors.

Intercept radar vectors for runway threeoneleft.

And all a linear combination of vectors are, they're just a

If every one of the vectors that represented this line, if