Deck 8: The Geometry of Vector Spaces

Question 1

Determine if the set of points is affinely dependent. If so, construct an affine dependence relation for the points.

Answer 1

D

Question 2

Find the barycentric coordinates of p with respect to the affinely independent set of points that precedes it.

Answer 2

B

Question 3

Provide an appropriate response.

Answer 3

C

Question 4

Provide an appropriate response.
Which of the following statements are true?

Question 5

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Question 6

Find the barycentric coordinates of p with respect to the affinely independent set of points that precedes it.

Question 7

Find the barycentric coordinates of p with respect to the affinely independent set of points that precedes it.

Question 8

Determine if the vector p is in Span S or aff S.

Question 9

Provide an appropriate response.

Question 10

Find the barycentric coordinates of p with respect to the affinely independent set of points that precedes it.

Question 11

Write y as an affine combination of the other points listed.

Question 12

Write y as an affine combination of the other points listed.

Question 13

Find the barycentric coordinates of p with respect to the affinely independent set of points that precedes it.

Question 14

Find the barycentric coordinates of p with respect to the affinely independent set of points that precedes it.

Question 15

Find the barycentric coordinates of p with respect to the affinely independent set of points that precedes it.

Question 16

Determine if the vector p is in Span S or aff S.

Question 17

Provide an appropriate response.

Question 18

Determine if the set of points is affinely dependent. If so, construct an affine dependence relation for the points.

Question 19

Provide an appropriate response.

Question 20

Determine if the vector p is in Span S or aff S.

Question 21

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Let (pos S)be the set of all positive combinations of the points of S. Which of the following statements are true?

Question 22

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Question 23

Provide an appropriate response

Question 24

Use the barycentric coordinates with respect to S to determine if the point p is inside, outside, on a face, or on the edge
of conv S which is a tetrahedron.

Question 25

Find the barycentric coordinates of p with respect to the affinely independent set of points that precedes it.

Question 26

Use the barycentric coordinates with respect to S to determine if the point p is inside, outside, on a face, or on the edge
of conv S which is a tetrahedron.

Question 27

Find the barycentric coordinates of p with respect to the affinely independent set of points that precedes it.

Question 28

Determine whether the point p is in the convex hull of S.

Question 29

Provide an appropriate response
Which of the following statements are true?

Question 30

Provide an appropriate response

Question 31

Use the barycentric coordinates with respect to S to determine if the point p is inside, outside, on a face, or on the edge
of conv S which is a tetrahedron.

Question 32

Use the barycentric coordinates with respect to S to determine if the point p is inside, outside, on a face, or on the edge
of conv S which is a tetrahedron.

Question 33

Determine whether the point p is in the convex hull of S.

Question 34

Provide an appropriate response

Question 35

Provide an appropriate response

Question 36

Sketch the graph of the convex hull of S.

Question 37

Sketch the graph of the convex hull of S.

Question 38

Find the barycentric coordinates of p with respect to the affinely independent set of points that precedes it.

Question 39

Provide an appropriate response

Question 40

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Question 41

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Question 42

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Question 43

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Which of the following statements are true? I: If A and B are convex sets then A + B is convex.
II: A four dimensional polytope always has the same number of vertices and edges.

A)II
B)Neither I or II
C)Both I and II
D)I

Question 44

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Question 45

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Question 46

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Question 47

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Question 48

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Question 49

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Question 50

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Let int S be the set of all interior points of S, and let cl S be the closure of S (S ∪ the set of all boundary points of S). Which of the following statements are true?
I: If S is convex, then int S is convex.
II: If S is convex, then cl S is convex.

A)II
B)Both I and II
C)Neither I or II
D)I

Question 51

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Question 52

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Which of the following statements are true? I: A polytope is the affine hull of a finite set of points.
II: An extreme point of a polytope P is any point in the convex hull of 2 vertices.

A)Neither I or II
B)II
C)I
D)Both I and II

Question 53

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Question 54

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Question 55

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Question 56

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Question 57

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