16.1.14. Let R = M2×2 (R) be the ring of two-by-two matrices with real entries. [0 b [a b] Let S = { | a, b = R} and T = { 0 a 00 [o of] b € R} . (a) Are T and S subrings of R? (b) Is T an ideal of S? Is T an ideal of R? Is S an ideal of R?
16.1.14. Let R = M2×2 (R) be the ring of two-by-two matrices with real entries. [0 b [a b] Let S = { | a, b = R} and T = { 0 a 00 [o of] b € R} . (a) Are T and S subrings of R? (b) Is T an ideal of S? Is T an ideal of R? Is S an ideal of R?
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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Question
![16.1.14. Let R = M2×2 (R) be the ring of two-by-two matrices with real entries.
[0 b
[a
b]
Let S = {
| a, b = R} and T
=
{
0 a
00
[o of] b € R} .
(a) Are T and S subrings of R?
(b) Is T an ideal of S? Is T an ideal of R? Is S an ideal of R?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff5fbaae5-8d47-4476-8095-8b380294ae7e%2Fff3e15b6-52ff-4d9b-bb4d-f72599bdbf91%2Fe221a4_processed.png&w=3840&q=75)
Transcribed Image Text:16.1.14. Let R = M2×2 (R) be the ring of two-by-two matrices with real entries.
[0 b
[a
b]
Let S = {
| a, b = R} and T
=
{
0 a
00
[o of] b € R} .
(a) Are T and S subrings of R?
(b) Is T an ideal of S? Is T an ideal of R? Is S an ideal of R?
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