M = {[a b] 1 a, b, c € 0} over the field F= R with standard addition and scalar multiplication of matrices. Recall Q represents the set of rational numbers and R is the set of real numbers. a. The set M is not a vector space over R. Identify and state all vector space axioms that fail or structurally are sound but do not necessarily result in vectors back in M, with an explanation. b. If M is unaltered, what scalar field could be used to satisfy all vector axioms? Explain in a complete sen- tence, or two.
M = {[a b] 1 a, b, c € 0} over the field F= R with standard addition and scalar multiplication of matrices. Recall Q represents the set of rational numbers and R is the set of real numbers. a. The set M is not a vector space over R. Identify and state all vector space axioms that fail or structurally are sound but do not necessarily result in vectors back in M, with an explanation. b. If M is unaltered, what scalar field could be used to satisfy all vector axioms? Explain in a complete sen- tence, or two.
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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![M
M = {[a b] ₁ a, b, cc Q}
over the field F = R with standard addition and scalar multiplication of matrices. Recall Q represents the set of
rational numbers and R is the set of real numbers.
a. The set M is not a vector space over R. Identify and state all vector space axioms that fail or structurally
are sound but do not necessarily result in vectors back in M, with an explanation.
b. If M is unaltered, what scalar field could be used to satisfy all vector axioms? Explain in a complete sen-
tence, or two,](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F66947364-781a-4c5b-9f23-45871f645082%2Fcb2effce-f87d-4298-9566-4cfd901a5f33%2Fmcl9k8r_processed.jpeg&w=3840&q=75)
Transcribed Image Text:M
M = {[a b] ₁ a, b, cc Q}
over the field F = R with standard addition and scalar multiplication of matrices. Recall Q represents the set of
rational numbers and R is the set of real numbers.
a. The set M is not a vector space over R. Identify and state all vector space axioms that fail or structurally
are sound but do not necessarily result in vectors back in M, with an explanation.
b. If M is unaltered, what scalar field could be used to satisfy all vector axioms? Explain in a complete sen-
tence, or two,
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