a b Consider M₂ (R) {[%d) | a, b, c, d = R с X Y (a) Show that I = { [ + ² ] | x₁yER} is a subring of M₂ (R). Y X Z Z (b) Is J = ZER an ideal of I? Justify your answer. Z Z = }, a ring under matrix addition and matrix mutiplication.
a b Consider M₂ (R) {[%d) | a, b, c, d = R с X Y (a) Show that I = { [ + ² ] | x₁yER} is a subring of M₂ (R). Y X Z Z (b) Is J = ZER an ideal of I? Justify your answer. Z Z = }, a ring under matrix addition and matrix mutiplication.
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
![Consider M₂ (R)
(a) Show that I
(b) Is J
{[
=
=
Z
2
{[d]
X
{[
Y
2
Z
=
X
ZER
a, b, c, d ER a ring under matrix addition and matrix mutiplication.
|x, y ≤R
R}
is a subring of M₂ (R).
an ideal of I? Justify your answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd6739906-8f9c-4dba-b43f-d82fd7c6b9c9%2F8b1a77b9-3b83-486a-8136-12b03510a89f%2Fybqhfs_processed.png&w=3840&q=75)
Transcribed Image Text:Consider M₂ (R)
(a) Show that I
(b) Is J
{[
=
=
Z
2
{[d]
X
{[
Y
2
Z
=
X
ZER
a, b, c, d ER a ring under matrix addition and matrix mutiplication.
|x, y ≤R
R}
is a subring of M₂ (R).
an ideal of I? Justify your answer.
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