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. Vis a vector space. Vis not a vector space, and Axioms 4 and 5 fail to hold. Vis not a vector space, and Axiom 7,8, 9 fails to hold. V is not a vector space, and Axiom 10 fails to hold. Vis not a vector space, and Axioms 2 and 3 fail to hold.

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. Vis a vector space. Vis not a vector space, and Axioms 4 and 5 fail to hold. Vis not a vector space, and Axiom 7,8, 9 fails to hold. V is not a vector space, and Axiom 10 fails to hold. Vis not a vector space, and Axioms 2 and 3 fail to hold.

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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