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Let $\mathbf{v}_{1}=\left[\begin{array}{l}{1} \\ {1}\end{array}\right], \mathbf{v}_{2}=\left[\begin{array}{l}{3} \\ {0}\end{array}\right], \mathbf{v}_{3}=\left[\begin{array}{l}{5} \\ {3}\end{array}\right],$ and $\mathbf{p}=\left[\begin{array}{l}{4} \\ {1}\end{array}\right] .$ Find a hyperplane $[f : d]$ (in this case, a line) that strictly separates $\mathbf{p}$ from $\operatorname{conv}\left\{\mathbf{v}_{1}, \mathbf{v}_{2}, \mathbf{v}_{3}\right\}$

Then, $f\left(v_{2}\right)=f\left(v_{3}\right)=9,$ and $f(p)=10,$ so any $d$ satisfying $9<d<10$ will work.

Calculus 3

Chapter 8

The Geometry of Vector Spaces

Section 4

Hyperplanes

Vectors

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Okay, so in this question, we want to find the hype we want to find. There exists a higher things which separates a one and beat so the heart abstain in this question, who all is given by three x one plus by X two months by two x three. Now we have to compete with distances for a one, and all of them is three times to give you six minus one minus. Two times five gives it 10. So that is this minus five f bulb a tuba Music three times three Giving mine plus one minus. Two times three Getting one of six. So that's four f o a. Three is it 23 times minus one using negative three plus six. So that's just three Now, if you will be one is equal to three times a week. Zero plus five minus two times minus one gives a prostitute That's seven. It will be true. Is it? Two? Three times one gives you three Meyers three minus two times by my studio plus four. So that's just four o. B. Three is equal to 23 times to deep six plus to minus two times 2 to 1. So that's six. So now you want to find a high plane who separates these values altogether, Separates this values and these. So if we draw one about High Plains where offenses even sued What f off X, he's a zero. So we just have this FX. So this thing is, if you 20 what you see is that out? How a one will lie a one lie How a one Spain, We'll lie above here. Well, like yeah. Oh, so a one state will live with this one. So if oh, explore gifted minds five lap that. But then everything else will, like low like a lotus plane, A rosy nose. So then we haven't separated a ones and the ones so instead, to separate them what we'll do these will set effort. This effort is equal to four in this case, in this case, this plane minus five plane. Well, that's just that was three plane that's re sign. We'll lie somewhere here it's the bigger bubble fo x Ah, he's even 23 and the modest five plane like just appear above that. Uh, if X by is into my file and then these tangle, of course. Libel, Otis. So just for one of them, okay. And so f o X bar is excuse six every moment on seven. So, yes, we found a high plane which can separate these two. But the problem is this point right here at eight. To and be to lie on this high thing. So there is not high plane that's strictly strip separate A and B, so the answer is no.

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