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Determine whether the set equipped with the given operations is a vector space. For those that are not vector spaces identify the vector space axioms that fail. The set of all pairs of real numbers of the form (x,0) with the standard operations on R°. O Vis not a vector space, and Axiom 7, 8, 9 fails to hold. O Vis not a vector space, and Axioms 2 and 3 fail to hold. O Vis not a vector space, and Axiom 10 fails to hold. O Vis not a vector space, and Axioms 4 and 5 fail to hold. O Vis a vector space.

Determine whether the set equipped with the given operations is a vector space. For those that are not vector spaces identify the vector space axioms that fail. The set of all pairs of real numbers of the form (x,0) with the standard operations on R°. O Vis not a vector space, and Axiom 7, 8, 9 fails to hold. O Vis not a vector space, and Axioms 2 and 3 fail to hold. O Vis not a vector space, and Axiom 10 fails to hold. O Vis not a vector space, and Axioms 4 and 5 fail to hold. O Vis a vector space.

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.2: Vector Spaces
Problem 37E: Let V be the set of all positive real numbers. Determine whether V is a vector space with the...
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Determine whether the set equipped with the given operations is a vector space. For those that are not vector spaces identify the vector space axioms that fail. The set of all pairs of real numbers of the form (x,0) with the standard operations on R. O Vis not a vector space, and Axiom 7, 8,9 fails to hold. O Vis not a vector space, and Axioms 2 and 3 fail to hold. O Vis not a vector space, and Axiom 10 fails to hold. O Vis not a vector space, and Axioms 4 and 5 fail to hold. O Vis a vector space.
Transcribed Image Text:Determine whether the set equipped with the given operations is a vector space. For those that are not vector spaces identify the vector space axioms that fail. The set of all pairs of real numbers of the form (x,0) with the standard operations on R. O Vis not a vector space, and Axiom 7, 8,9 fails to hold. O Vis not a vector space, and Axioms 2 and 3 fail to hold. O Vis not a vector space, and Axiom 10 fails to hold. O Vis not a vector space, and Axioms 4 and 5 fail to hold. O Vis a vector space.
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