4. Is M₂ (R) a field? Justify. I 5. Show that T = = { [ ² ] 12,9₁² € R} i 2 is a subring of M₂ (R).
4. Is M₂ (R) a field? Justify. I 5. Show that T = = { [ ² ] 12,9₁² € R} i 2 is a subring of M₂ (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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answer no.5
![Let M₂ (R) be the set of 2 x 2 matrices with real number entries, i.e.,
M₂(R) = {[a b]a,b,c,d ER}.
Define matrix addition and matrix multiplication in M₂(R) as follows
a1
b₁
az b₂
a₁ + a₂ b₁ + b₂
=
[
C1
d₁
0₂ d₂
;] + [
][
b₁ az b₂
d₂
=
a₁a₂+ b₁c₂ a₁b₂ + b1d₂
c₁a₂+d₂c₂ c₁b₂+did₂
d₁ C₂
01
C1
].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd1c653e3-7876-48cf-8145-f982de6a0d95%2F807aa614-7e5d-4341-a35b-431d52c087a6%2Fa8iv92o_processed.png&w=3840&q=75)
Transcribed Image Text:Let M₂ (R) be the set of 2 x 2 matrices with real number entries, i.e.,
M₂(R) = {[a b]a,b,c,d ER}.
Define matrix addition and matrix multiplication in M₂(R) as follows
a1
b₁
az b₂
a₁ + a₂ b₁ + b₂
=
[
C1
d₁
0₂ d₂
;] + [
][
b₁ az b₂
d₂
=
a₁a₂+ b₁c₂ a₁b₂ + b1d₂
c₁a₂+d₂c₂ c₁b₂+did₂
d₁ C₂
01
C1
].
![4. Is M₂ (R) a field? Justify.
I Y
5. Show that T =
- {[ 8 ] |z, y, z € R} is a subring of M2 (R).
2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd1c653e3-7876-48cf-8145-f982de6a0d95%2F807aa614-7e5d-4341-a35b-431d52c087a6%2Ftnomte_processed.png&w=3840&q=75)
Transcribed Image Text:4. Is M₂ (R) a field? Justify.
I Y
5. Show that T =
- {[ 8 ] |z, y, z € R} is a subring of M2 (R).
2
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