Which of the following six sets are subrings of M(R)? Which ones have an identity? 0 0 (a) All matrices of the form (8 5) with reQ. (b) All matrices of the form (c) All matrices of the form (d) All matrices of the form (a b) 0 Ca a a with a, b, cЄZ. b with a, b, c = R. 0 with a Є R. 0 with a ЄR. (e) All matrices of the form a (69) (f) All matrices of the form 0 (a) with a ЄR. 0

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter10: Matrices
Section10.CR: Chapter 10 Review
Problem 11CR
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Which of the following six sets are subrings of M(R)? Which ones have an identity?
0
0
(a) All matrices of the form
(8 5)
with reQ.
(b) All matrices of the form
(c) All matrices of the form
(d) All matrices of the form
(a b)
0
Ca
a
a
with a, b, cЄZ.
b
with a, b, c = R.
0
with a Є R.
0
with a ЄR.
(e) All matrices of the form
a
(69)
(f) All matrices of the form
0
(a)
with a ЄR.
0
Transcribed Image Text:Which of the following six sets are subrings of M(R)? Which ones have an identity? 0 0 (a) All matrices of the form (8 5) with reQ. (b) All matrices of the form (c) All matrices of the form (d) All matrices of the form (a b) 0 Ca a a with a, b, cЄZ. b with a, b, c = R. 0 with a Є R. 0 with a ЄR. (e) All matrices of the form a (69) (f) All matrices of the form 0 (a) with a ЄR. 0
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