Delermine whetner the set, togetner with the inidicated operations, Is a vector space. I1 It is not, then ldentily one of the vector space axiorms trnat Talis. The set {(x, y): x 2 8, y 2 7} O The set is a vector space. O The set is not a vector space because it is not closed under addition. O The set is not a vector space because the commutative property of addition is not satisfied. O The set is not a vector space because the associative property of addition is not satisfied. O The set is not a vector space because it is not closed under scalar multiplication.

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Determine whether the set, together with the indicated operations, is a vector space. If it is not, then identify one of the vector space axioms that fails.
The set
{(x, y): x 2 8, y > 7}
O The set is a vector space.
The set is not a vector space because it is not closed under addition.
The set is not a vector space because the commutative property of addition is not satisfied.
O The set is not a vector space because the associative property of addition is not satisfied.
The set is not a vector space because it is not closed under scalar multiplication.
O O O
Transcribed Image Text:Determine whether the set, together with the indicated operations, is a vector space. If it is not, then identify one of the vector space axioms that fails. The set {(x, y): x 2 8, y > 7} O The set is a vector space. The set is not a vector space because it is not closed under addition. The set is not a vector space because the commutative property of addition is not satisfied. O The set is not a vector space because the associative property of addition is not satisfied. The set is not a vector space because it is not closed under scalar multiplication. O O O
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