Dean) Define F4 to be the set of all 2 x 2 matrices F₁ = {[8 a+b] : ab € P₂} . F4= Prove that F4 is a commutative ring whose operations are matrix addition and matrix multiplication. Prove that F4 is a field having exactly 4 elements.
Dean) Define F4 to be the set of all 2 x 2 matrices F₁ = {[8 a+b] : ab € P₂} . F4= Prove that F4 is a commutative ring whose operations are matrix addition and matrix multiplication. Prove that F4 is a field having exactly 4 elements.
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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![*3.19 (R. A. Dean) Define F4 to be the set of all 2 x 2 matrices
F4=
F₁ = {[8 a+b] : a.b @P₂} .
a,
Prove that F4 is a commutative ring whose operations are matrix addition and
matrix multiplication.
(i)
(ii) Prove that F4 is a field having exactly 4 elements.
(iii)
Show that I4 is not a field.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb94def8c-dd78-4ff0-b08a-573f4a690a32%2Fcb24fcfa-a6bf-4085-abc1-fc657cba8b54%2F9gieg4a_processed.jpeg&w=3840&q=75)
Transcribed Image Text:*3.19 (R. A. Dean) Define F4 to be the set of all 2 x 2 matrices
F4=
F₁ = {[8 a+b] : a.b @P₂} .
a,
Prove that F4 is a commutative ring whose operations are matrix addition and
matrix multiplication.
(i)
(ii) Prove that F4 is a field having exactly 4 elements.
(iii)
Show that I4 is not a field.
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