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 3 x 3 matrices of the form a 0 0 0 b d e 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 an additive identity does not exist. O The set is not a vector space because an additive inverse does not exist. O The set is not a vector space because it is not closed under scalar multiplication.

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 3 × 3 matrices of the form
a 0 0
0 b c
d e
with the standard operations
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 an additive identity does not exist.
The set is not a vector space because an additive inverse does not exist.
The set is not a vector space because it is not closed under scalar multiplication.
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 3 × 3 matrices of the form a 0 0 0 b c d e with the standard operations 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 an additive identity does not exist. The set is not a vector space because an additive inverse does not exist. The set is not a vector space because it is not closed under scalar multiplication.
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