Answered: Question 6 For each of the relations on… | bartleby

Elementary Linear Algebra (MindTap Course List)

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Linear Transformations

Section6.2: The Kernewl And Range Of A Linear Transformation

Problem 64E

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Question 6
For each of the relations on A ={1, 2, 3} below,
R =
{(1, 1), (1, 3), (3, 3)},
S = {(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (3, 3)},
Т 3D {(1, 2), (2, 1), (2, 2)},
determine whether they are reflexive, symmetric, or transitive. Provide the reasons if
they are not reflexive, symmetric, or transitive.

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Let T be a linear transformation from R3 into R such that T(1,1,1)=1, T(1,1,0)=2 and T(1,0,0)=3. Find T(0,1,1)
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Describe the reflection of △FGH△FGH with vertices F(−3, 2), G(−4, −1)F(-3, 2), G(-4, -1), and H(−6, −1)H(-6, -1), to its image △F′G′H△F′G′H′ with vertices F′(2, −3), G′(−1, −4)F′(2, -3), G′(-1, -4), and H′(−1, −6)H′(-1, -6). Use decimals, if necessary. (x, y) → ( , ) ---- I don't know how to put it into coordinates.
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Let A = {0,1,2,3} and R be the relation on A given by R = {(0,0),(0,2),(1,1),(1,2),(2,1),(2,0),(3,1),(2,2),(2,3),(3,2)}. Is R reflexive, symmetric, transitive, antisymmetric?
Let y={0,1,2} and 2={0,1} and define a relation r from a to b as follows: Given any (x,y)€ Y×Z. (x,y)€ R means that x+y/2 is an integer 1. State explicitly which ordered pairs are in YxZ and which are in R. 2. Is 1 R 0? Is 2 R 0? Is 2 R 1? 3. What are the domain are co-domain of R?
Define relations R 1 , … , R 6 on { 1 , 2 , 3 , 4 } by R 1 = { ( 2 , 2 ) , ( 2 , 3 ) , ( 2 , 4 ) , ( 3 , 2 ) , ( 3 , 3 ) , ( 3 , 4 ) } , R 2 = { ( 1 , 1 ) , ( 1 , 2 ) , ( 2 , 1 ) , ( 2 , 2 ) , ( 3 , 3 ) , ( 4 , 4 ) } , R 3 = { ( 2 , 4 ) , ( 4 , 2 ) } , R 4 = { ( 1 , 2 ) , ( 2 , 3 ) , ( 3 , 4 ) } , R 5 = { ( 1 , 1 ) , ( 2 , 2 ) , ( 3 , 3 ) , ( 4 , 4 ) } , R 6 = { ( 1 , 3 ) , ( 1 , 4 ) , ( 2 , 3 ) , ( 2 , 4 ) , ( 3 , 1 ) , ( 3 , 4 ) } , Which of the following statements are correct? Check ALL correct answers below. A. R 2 is not transitive B. R 4 is antisymmetric C. R 5 is transitive D. R 6 is symmetric E. R 3 is transitive F. R 3 is reflexive G. R 3 is symmetric H. R 2 is reflexive I. R 4 is transitive J. R 5 is not reflexive K. R 4 is symmetric L. R 1 is not symmetric M. R 1 is reflexive
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Problem 9For the following equivalence relation describe the corresponding partition without anyredundancy or reference to the name of the relation. Let ∼be the relation on R−{0}definedby x ∼y if and only if xy > 0, for all x, y ∈R−{0}.

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