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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 of all fourth-degree polynomials with the standard operations O The set is a vector space. The set is not a vector space because it is not closed under addition. 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 an additive inverse does not exist. O The set is not a vector space because the distributive property of scalar multiplication is not satisfied.

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 of all fourth-degree polynomials with the standard operations O The set is a vector space. The set is not a vector space because it is not closed under addition. 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 an additive inverse does not exist. O The set is not a vector space because the distributive property of scalar multiplication is not satisfied.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.1: Vector Spaces And Subspaces
Problem 2EQ
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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 of all fourth-degree polynomials with the standard operations 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 associative property of addition is not satisfied. O The set is not a vector space because an additive inverse does not exist. O The set is not a vector space because the distributive property of scalar multiplication is not satisfied.
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 of all fourth-degree polynomials with the standard operations 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 associative property of addition is not satisfied. O The set is not a vector space because an additive inverse does not exist. O The set is not a vector space because the distributive property of scalar multiplication is not satisfied.
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