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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 4 x 4 matrices of the form 0 a ac COCa b b0 c babi] 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. The set is not a vector space because it does not satisfy the associative property of addition. The set is not a vector space because a scalar identity does not exist. O The set is not a vector space because it does not satisfy the distributive property.

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 4 x 4 matrices of the form 0 a ac COCa b b0 c babi] 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. The set is not a vector space because it does not satisfy the associative property of addition. The set is not a vector space because a scalar identity does not exist. O The set is not a vector space because it does not satisfy the distributive property.

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 4 x 4 matrices of the form 0 a a c COCa b a b 1 with the standard operations 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 it does not satisfy the associative property of addition. The set is not a vector space because a scalar identity does not exist. The set is not a vector space because it does not satisfy the distributive property.
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 4 x 4 matrices of the form 0 a a c COCa b a b 1 with the standard operations 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 it does not satisfy the associative property of addition. The set is not a vector space because a scalar identity does not exist. The set is not a vector space because it does not satisfy the distributive property.
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