Let K be a field. Consider the following set {(::)- a1 0 R:= a2 a1 (a) Show that (R, +) with the matrix addition as operation has a commutative subgroup of (K*, is. (b) Show for all " A, BER: A, BER = A.BER
Let K be a field. Consider the following set {(::)- a1 0 R:= a2 a1 (a) Show that (R, +) with the matrix addition as operation has a commutative subgroup of (K*, is. (b) Show for all " A, BER: A, BER = A.BER
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
plz provide answer for part b
![Let K be a field. Consider the following set
{(:)
a1 0
R:=
E K²x2 :
a2 a1
(a) Show that (R, +) with the matrix addition as operation has a commutative subgroup of
(K2
is.
(b) Show for all "A, BER:
A, BER = A · BER
(K²x2,+,·),
(c) Using (a).(b) and the ring properties of
that (R, +, ) with the matrix addition and
matrix multiplication as linkage "
gen forms a commutative ring with unity.
It is important to avoid proving ring properties directly
(K²x2, +,·),
follows directly from (a),(b) or the ring properties of
can be derived
(d) Show that (R, +, ) is not a zero divisor.
(e) Let (R+, ) the unit group of (R, +, ·). Show it:
A E R + A E RA det A +0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8e5b1a56-3032-449a-acc6-d2196fb84e38%2F51bb31ab-1bf7-4aa6-b530-be96cb843073%2Fyyaa93m_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let K be a field. Consider the following set
{(:)
a1 0
R:=
E K²x2 :
a2 a1
(a) Show that (R, +) with the matrix addition as operation has a commutative subgroup of
(K2
is.
(b) Show for all "A, BER:
A, BER = A · BER
(K²x2,+,·),
(c) Using (a).(b) and the ring properties of
that (R, +, ) with the matrix addition and
matrix multiplication as linkage "
gen forms a commutative ring with unity.
It is important to avoid proving ring properties directly
(K²x2, +,·),
follows directly from (a),(b) or the ring properties of
can be derived
(d) Show that (R, +, ) is not a zero divisor.
(e) Let (R+, ) the unit group of (R, +, ·). Show it:
A E R + A E RA det A +0
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