Refer a friend and earn $50 when they subscribe to an annual planRefer Now

Get the answer to your homework problem.

Try Numerade Free for 30 Days

Like

Report

In Exercises 16 and $17,$ mark each statement True or False. Justify each answer. a. A cube in $\mathbb{R}^{3}$ has exactly five facets.b. A point $\mathbf{p}$ is an extreme point of a polytope $P$ if and only if $\mathbf{p}$ is a vertex of $P .$ c. If $S$ is a nonempty compact convex set and a linear functional attains its maximum at a point $\mathbf{p}$ , then $\mathbf{p}$ is an extreme point of $S$ .d. $\mathrm{A} 2$ -dimensional polytope always has the same number of vertices and edges.

a) Falseb) truec) Falsed) true

Calculus 3

Chapter 8

The Geometry of Vector Spaces

Section 5

Polytopes

Vectors

Oregon State University

Harvey Mudd College

University of Nottingham

Idaho State University

Lectures

02:56

In mathematics, a vector (…

06:36

00:48

Mark each statement True o…

07:49

In Exercises 25 and $26,$ …

07:24

02:50

In Exercises 11 and $12,$ …

02:29

In Exercises 21 and $22,$ …

01:51

In Exercises 45-47, determ…

02:09

In Exercises 15 and $16,$ …

01:35

In Exercises 17 and $18,$ …

09:01

06:10

In Exercises 19 and 20, V …

forgiven a statement and were asked to market tour false and then to just fire answer in part a. The statement is Cube in. Our three has exactly five facets. The statement is false. A number of facets of a cube in our three is six because in our three, a facet is the same as a square face. Now, in part B, the statement is a point. P is an extreme point of a poly tope if and only if p is a vertex of the politics. This statement is true. This is a direct consequence of the're um 14. In the book, the serum says that a point of a poly tope is an extreme point if and only if it's a vertex and definitely if it lies in the profile now in part C were given the statement if s is a non empty, compact convex set and a linear functional attains its maximum at a point p then P is an extreme point of s. This is false. So while the maximum is always attained at some extreme point maybe other points that are not extreme points I wish the maximum is attained. In fact, there are examples given in the book. I would say, for example, look, at example three part C. After the're, um 16. We see that the linear functional attendance maximum value at to extreme points, but then also at every point in the complex whole of these extreme points and these points in the comics whole are not. Extreme points now in Part D were given the statement a two dimensional Polito always has the same number of Vergis is and edges. This statement is true to see why. Consider Oilers formula so by Oilers formula checking in to be to We get that for a two dimensional polito f zero of call this P and then minus If one of P is equal to one plus negative one to the first, which is zero So it follows F zero p is equal to F one of p. Therefore, the number of Vergis is for this play. Tope is always the same as the number of edges

View More Answers From This Book

Find Another Textbook

In mathematics, a vector (from the Latin word "vehere" meaning &qu…

In mathematics, a vector (from the Latin "mover") is a geometric o…

Mark each statement True or False. Justify each answer.a. A set is conve…

In Exercises 25 and $26,$ mark each statement True or False. Justify each an…

In Exercises 11 and $12,$ mark each statement True or False. Justify each an…

In Exercises 21 and $22,$ mark each statement True or False. Justify each an…

In Exercises 45-47, determine whether the statement is true or false. Justif…

In Exercises 15 and $16,$ mark each statement True or False. Justify each an…

In Exercises 17 and $18,$ mark each statement True or False. Justify each an…

In Exercises 19 and 20, V is a vector space. Mark each statement True or Fal…

01:21

If a trinomial is multiplied by a binomial, how many times must you multiply…

02:24

The length of the shorter leg, a, of a right triangle is 6 centimeters less …

03:11

Find an example of a bounded convex set $S$ in $\mathbb{R}^{2}$ such that it…

03:08

In Exercises $21-26,$ prove the given statement about subsets $A$ and $B$ of…

03:25

Repeat Exercise 25 with $\mathbf{v}_{1}=\left[\begin{array}{r}{1} \\ {2} \\ …

07:52

Let $L$ be the line in $\mathbb{R}^{2}$ through the points $\left[\begin{arr…

05:41

Let $\mathbf{v}_{1}=\left[\begin{array}{r}{2} \\ {0} \\ {-1} \\ {2}\end{arra…

09:15

In Exercises 19 and $20,$ all vectors are in $\mathbb{R}^{n} .$ Mark each st…

03:55

Find an SVD of each matrix [Hint: In Exercise 11, one choice for $U$ is $\le…

01:31

In $\mathbb{R}^{2},$ let $S=\left\{\left[\begin{array}{l}{0} \\ {y}\end{arra…

92% of Numerade students report better grades.

Try Numerade Free for 30 Days. You can cancel at any time.

Annual

0.00/mo 0.00/mo

Billed annually at 0.00/yr after free trial

Monthly

0.00/mo

Billed monthly at 0.00/mo after free trial

Earn better grades with our study tools:

Textbooks

Video lessons matched directly to the problems in your textbooks.

Ask a Question

Can't find a question? Ask our 30,000+ educators for help.

Courses

Watch full-length courses, covering key principles and concepts.

AI Tutor

Receive weekly guidance from the world’s first A.I. Tutor, Ace.

30 day free trial, then pay 0.00/month

30 day free trial, then pay 0.00/year

You can cancel anytime

OR PAY WITH

Your subscription has started!

The number 2 is also the smallest & first prime number (since every other even number is divisible by two).

If you write pi (to the first two decimal places of 3.14) backwards, in big, block letters it actually reads "PIE".

Receive weekly guidance from the world's first A.I. Tutor, Ace.

Mount Everest weighs an estimated 357 trillion pounds

Snapshot a problem with the Numerade app, and we'll give you the video solution.

A cheetah can run up to 76 miles per hour, and can go from 0 to 60 miles per hour in less than three seconds.

Back in a jiffy? You'd better be fast! A "jiffy" is an actual length of time, equal to about 1/100th of a second.