WE WANT TO FlGURE OUT THlS...

And we can show very easily

And I think we'd all best face the truth.

AP exam but my point here to make sure we all are understanding what's going on.

Well, we would have to show that this could actually imply two different triangles.

We can show and they have the same solution set.

In it, we had to kind of brush off our trig identities.

So to show that just these three vectors by themselves span our column space, we just have to show that I can represent a3 and a5 as linear combinations of a1, a2, and a4.

Now in order to show that I can always do this, we have to show that for this combination there's always some x1, x2, and x4 that satisfy this.

Now they ask us identify the equation that represents the relationship.

They're saying that the radius is 12 5 not the diameter, so there we make it very clear,

Let's make it clear

In the next one we'll show that these three guys also span your column space.

And if we can get rid of them we can show that these guys can be represented as linear combinations of the other, then we can get rid of them.

An interesting way to prove it, and you can look at it just by eyeballing it, is if we can show that this triangle is congruent to this triangle and that these 2 angles right over here correspond to each other then they have to be the same and they'll be supplementary and they'll be 90 degrees so let's just prove it to ourselves

And we know that these triangles, these triangles are all going to be congruent to each other and there's multiple ways if we could show it

We could even switch around the variable names if we want just to show you that they don't have to be a's and b's.

Well, let's explore that.

So let's explore what this is a little bit.

Let's get that straight.

Let's get something straight.

He recognized the mutual advantage of pooling forces.

It's obvious to everybody. Especially to him.

Now, the next thing to prove that they are a basis, is to show that all of the other column vectors can be represented as multiples of these three guys.

The whole point of this video is to clarify the motivation for calling them even or odd functions.

Just to make it clear, even this ambiguous, maybe we put a line over to show, that is our level of precision, that we have 2 significant digits.

So here we say the domain is equal to do little brackets, that shows kind of the set of what x's apply.

so we're able to using constructing this triangle here we're able to both show its a similar and to construct this larger isosceles triangle to show

So, I want to give you the three things that we teach everybody.

I am always grateful to everyone in Give N.

Permit us to illustrate.

And just to make it clear, you know,

Let's figure out what that minimum speed is

Let's explore this equation a little bit.

Dr. Campbell, now let's get this thing straight.

All right. Let's get this business straight.

Now the next requirement for a basis, we checked this one off, is to show that a1 a2 and an, that their span equals the column space of A.

And that's certainly something that anybody can look into.

Whoever of you wants to become first among you, shall be bondservant of all.

And whosoever of you will be the chiefest, shall be servant of all.

Stephanie White I'm going to let her introduce herself to everybody.

SW This is Einstein. Can you tell everyone hi ?

Let's also figure out some other interesting things.

How is that even possible? Let's break it down.

We already figured it out, our constant horizontal velocity