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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 2 x 2 matrices of the form a 2 2 b with the standard matrix addition and scalar multiplication. O Vis not a vector space, and Axioms 1, 4, 5, 6 fail to hold. O Vis not a vector space, and Axioms 1, 5, 6 fail to hold. O Vis not a vector space, and Axioms 1, 2, 3 fail to hold. O Vis not a vector space, and Axioms 6 - 9 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 2 x 2 matrices of the form a 2 2 b with the standard matrix addition and scalar multiplication. O Vis not a vector space, and Axioms 1, 4, 5, 6 fail to hold. O Vis not a vector space, and Axioms 1, 5, 6 fail to hold. O Vis not a vector space, and Axioms 1, 2, 3 fail to hold. O Vis not a vector space, and Axioms 6 - 9 fail to hold. O Vis a vector space.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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 2 x 2 matrices of the form a 2 2 b with the standard matrix addition and scalar multiplication. O Vis not a vector space, and Axioms 1, 4, 5, 6 fail to hold. O Vis not a vector space, and Axioms 1, 5, 6 fail to hold. O Vis not a vector space, and Axioms 1, 2, 3 fail to hold. O Vis not a vector space, and Axioms 6 - 9 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 2 x 2 matrices of the form a 2 2 b with the standard matrix addition and scalar multiplication. O Vis not a vector space, and Axioms 1, 4, 5, 6 fail to hold. O Vis not a vector space, and Axioms 1, 5, 6 fail to hold. O Vis not a vector space, and Axioms 1, 2, 3 fail to hold. O Vis not a vector space, and Axioms 6 - 9 fail to hold. O Vis a vector space.
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