in-mathbbr2-let-sleftleftbeginarrayl0-yendarrayright-0-leq-y1right-cupleftleftbeginarrayl2-0endarray

Question

In $\mathbb{R}^{2},$ let $S=\left\{\left[\begin{array}{l}{0} \ {y}\end{array}ight] : 0 \leq y<1ight\} \cup\left\{\left[\begin{array}{l}{2} \ {0}\end{array}ight]ight\} .$ Describe (or sketch) the convex hull of $S .$

Lucía Guerrero · Accepted Answer

So I have illustrated in green the set s that we were given on to find its comics. Hall. Remember that if we pick any two points in the set, uh, then the lines have been joining them. Must be in the comics hole so we can do in any point on this vertical segment with the point to common zero on this, we&#x27;re going to find a lot off lying segments that we&#x27;re going to cover all these triangular region on all the segments must be in the comics whole of s, uh, avoiding this black dotted lied. So we can describe the comics whole off iss as what I draw. As a region of course, offices filled on this set can be described as the victories whose first card in it is greater than a report. ASI wrote on less than a recorded too, whose second coordinate is greater than or equal to zero on a strictly less uh, minus one half times X plus one. And this is the question of the black dotted line onto the set. We&#x27;re going to add the vector to Syria

Wen Zheng · Answer

The problem is sketch the solid described about giving qualities. It is between zero and pi over to the years between our and too. So we can sketch too solid as follows, not his style. Art is the call to squat narrative Ex squire us Why square over half Are you going to see this? X square plus y square is equal to C scoring, which is our corn. This Look This Oh here it is the last time too. So two on three days between zero and pi over too over half It&#x27;s art. This is a solid it describe it about given qualities from here here.

Paul Teng · Answer

Okay, so this problem wants you to plot this volume that is described by these two inequalities. All right, so looking, let&#x27;s look at the first This inequality first, So are has to be less than able to Z, which has to be less than are able to to looking at this part C is less than or equal to two. This tells me that this region is bounded above by the plane. Z equals two. So it was founded above by horizontal plane. Z equals a to this part, are is less than or equal to Z. Well, that tells me that this is bounded below by the equation or equals Z. And this is an equation for coal. And one last thing that also tells me is that the fatum is from zero to pi over two. So the only part that we&#x27;re going to be seeing for this volume is gonna be in between the positive X axis and the positive y axis. Because China is the angle rotates respect to deposit X axis in the counter clockwise direction. All right, so now that we have our information, we can go ahead and plot this region so I&#x27;m gonna draw multiple straight lines. Tell me so I get a sense off from try it. So it is done it above by plane. Z equals to remember, So we can&#x27;t draw anything above the was A to it&#x27;s long been connect. This is also bound to be low by a comb. So draw my cone Now my comb. Uh, yeah, you go. So I&#x27;m gonna go head. Go ahead and get rid of these parts. And there you go. This is what your colon should look like. Well, I guess 1/4 of a cone since it&#x27;s bounded below by r equals e again valley below by article Suzie and bounded about by Z equals to tell.

Paul Teng · Answer

Okay, so this problem wants you to sketch service with the falling restrictions. The following restrictions are has to be in between. The two data has to be in between a Pirated a pirate too. And he has to be from 0 to 1. Okay, So looking at our and data, you know, from our if this was looking at an X Y plane, so with polar coordinates R is going to be the rays. The radius on a distance from the pole and data is going to be the angle with respect to the positive X axis for which it rotates where the point is going to be so if they don&#x27;t, it says from native prior to departure tomb. But they dont pirate too, meaning that it rotates nine degrees or pirate to radiance from the X axis. And with the radius of two, the rotation will look something look something like this. So that&#x27;s from zero pi over two. And if you will go from zero to native power to it would go into would go clockwise instead of counterclockwise. So it looks something like about. So that&#x27;s that covers the region off our It&#x27;s a region inside this circle everything in between from 0 to 2 for our and negative Pirated part a twofer data. And finally, the last restraint is that Z has to be greater. Has be in between zeroing one. So this right here on the X y plane This is for one c. This is for when z is this is one Z is equal to zero and Z axes here. So Z value of one would be right here. So everything just disease the directive distance from the X y plane. So everything just shifts up a value of one. So we want to shift everything from just shift everything of value one, we get a region region. I would look something look something like this better something like this thing go. And this is essentially a cylinder part of a cylinder that&#x27;s been cut off in every and all the restricted restrains all restricted regions. That is it

Stark Ledbetter · Answer

So the problem wants you to sketch the solid given by these three inequalities. Um So we have row fee and data. So we&#x27;re in spherical coordinates. Okay? Um And we&#x27;ll just we&#x27;ll start drawing coordinate system. I like to do it this way. You can do it anyway. As long as you&#x27;re coordinate system is right handed, it follows the right hand roll. Um Let&#x27;s start with a fee. Since that&#x27;s the strangest one. This is the angle with the positive Z. Axis. So here&#x27;s the Z axis, positive Z axis. We want to go up to pi over three or 60 degrees. So we&#x27;re going like just that inequality would be would be this cone, We go down 60° this way or this would be 30°. Okay. And then what are the other constraints? Um data, same as with polar coordinates between zero and pi. So angle with the positive X. Axis. So we&#x27;re going in the xy plane there. So it&#x27;s on the back half of this graph. If you imagine going into the paper. Um So like cut off that cone at the Xz plane. It&#x27;s a little bit hard to show you because I can&#x27;t show you my hands here but cut it off at the exit plane. And then row is distance from the origin. So that means we&#x27;re going to start it too And go to four. So what we have is we have like these fears intersecting we&#x27;re not coming out of the page. We&#x27;re just staying on the back half and we have the cone. So I don&#x27;t know how well I can sketch this but it goes back there and these are spheres. So it&#x27;s like it&#x27;s like the top layer of ice cream on an ice cream cone, half the ice cream car the back half. If that makes sense. Um Maybe a better sketch would be over here. So we want half half of a cone where the cone is cut off by this sphere of radius to and also this, so this is a triangle. Yeah that would be the rest of the car. But we just want the topper.

Linda Hand · Answer

Yeah. Okay. Uh we&#x27;re going to describe what this is a picture of. So first of all notice it doesn&#x27;t say anything about data, so data is 0 to 2 pi so it&#x27;s all the way around. So if you just looked at row equals one, That&#x27;s a sphere of Radius one. And because that is everything and it&#x27;s the sphere all the way around. Okay. Okay. So then if you look at row equals two, that&#x27;s a sphere of radius too. So it&#x27;s outside here. All right, so what we have so far is uh row in between one and two. So it&#x27;s outside the sphere of Radius one, but inside the sphere of radius too. So like it&#x27;s a hollow chocolate ball. Okay. The inside part is taken now. Okay then fee between pi over two and pi here&#x27;s fee equal zero. Here&#x27;s fee equals pi over two. Here&#x27;s fee equals pi over pie. So we&#x27;re only looking at this part. Mhm. So we&#x27;re just looking at the bottom half here, so it&#x27;s the bottom half. Oh maybe like a cantaloupe cut open, okay with the stuff in the middle of taking out like that? The rind of a half a cantaloupe. Oh

Problem

Describe the convex hull of the set $S$ of points…

Problem 1 Easy Difficulty

In $\mathbb{R}^{2},$ let $S=\left\{\left[\begin{array}{l}{0} \\ {y}\end{array}\right] : 0 \leq y<1\right\} \cup\left\{\left[\begin{array}{l}{2} \\ {0}\end{array}\right]\right\} .$ Describe (or sketch) the convex hull of $S .$

Answer

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David C. Lay, Steven R. Lay, Judi J. McDonald

Linear Algebra and Its Applications

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Linear Algebra and Its Applications

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David C. Lay, Steven R. Lay, Judi J. McDonaldLinear Algebra and Its Applications

Anna Marie V.

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David C. Lay, Steven R. Lay, Judi J. McDonald

Linear Algebra and Its Applications