both b anc c if possible 2.b) Let G be the set of all 2x2 matrices [a b], a, b eR and a² + b² +0. Show that (G,*)where is the matrix multiplication forms a group.c) Let (G,) be a group. Then (G,) is abelian if and only if (ab)² = a² + b² for all a, b e G.

Answered: Image /qna-images/answer/9857f2d1-5b61-42da-85bb-f16d34b0baad.jpg

Answered: a,b eR and a² + b² #0. Show that (G,*)…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter2: Matrices

Section2.1: Operations With Matrices

Problem 76E

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15. Repeat Exercise with, the multiplicative group of matrices in Exercise of Section. 14. Let be the multiplicative group of matrices in Exercise of Section, let under multiplication, and define by a. Assume that is an epimorphism, and find the elements of. b. Write out the distinct elements of. c. Let be the isomorphism described in the proof of Theorem, and write out the values of.
2. Show that is a normal subgroup of the multiplicative group of invertible matrices in .
Prove or disprove that the set of all diagonal matrices in Mn() forms a group with respect to addition.
Show that the matrix below does not have an LU factorization. A=0110
The elements of the multiplicative group G of 33 permutation matrices are given in Exercise 35 of section 3.1. Find the order of each element of the group. (Sec. 3.1,35) A permutation matrix is a matrix that can be obtained from an identity matrix In by interchanging the rows one or more times (that is, by permuting the rows). For n=3 the permutation matrices are I3 and the five matrices. (Sec. 3.3,22c,32c, Sec. 3.4,5, Sec. 4.2,6) P1=[ 100001010 ] P2=[ 010100001 ] P3=[ 010001100 ] P4=[ 001010100 ] P5=[ 001100010 ] Given that G={ I3,P1,P2,P3,P4,P5 } is a group of order 6 with respect to matrix multiplication, write out a multiplication table for G.

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a,b eR and a² + b² #0. Show that (G,*) b) Let G be the set of all 2x2 matrices where * is the matrix multiplication forms a group. c) Let (G,+) be a group. Then (G,+) is abelian if and only if (a - b)² = a² + b² for all a, b e G.

a,b eR and a² + b² #0. Show that (G,) b) Let G be the set of all 2x2 matrices where is the matrix multiplication forms a group. c) Let (G,+) be a group. Then (G,+) is abelian if and only if (a - b)² = a² + b² for all a, b e G.