IF P= DF-CB find the value of the followingANSANS1P116P232P127P31%3D%3DP138P32%3D%3D4219P33%3DP22%3DII Given the matrices below-[] -[] [:]15325A =4B =84C =5684561295-8E =F=D =-5-2-6-3-9-81-7

Answered: Image /qna-images/answer/23fd0fde-5e3a-4932-9d41-cf9d101cbd01.jpg

Answered: IF P= DF-CB find the value of the…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.6: Matrices

Problem 11E: 11. Find two nonzero matrices and such that.

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Let A,D, and P be nn matrices satisfying AP=PD. Assume that P is nonsingular and solve this for A. Must it be true that A=D?
Consider the matrices R=[ 0110 ] H=[ 1001 ] V=[ 1001 ] D=[ 0110 ] T=[ 0110 ] in GL(2,), and let G={ I2,R,R2,R3,H,D,V,T }. Given that G is a group of order 8 with respect to multiplication, write out a multiplication table for G. Sec. 3.3,22b,32b Find the center Z(G) for each of the following groups G. b. G={ I2,R,R2,R3,H,D,V,T } in Exercise 36 of section 3.1. Find the centralizer for each element a in each of the following groups. b. G={ I2,R,R2,R3,H,D,V,T } in Exercise 36 of section 3.1 Sec. 4.1,22 22. Find an isomorphism from the octic group D4 in Example 12 of this section to the group G={ I2,R,R2,R3,H,D,V,T } in Exercise 36 of Section 3.1. Sec. 4.6,14 14. Let G={ I2,R,R2,R3,H,D,V,T } be the multiplicative group of matrices in Exercise 36 of section 3.1, let G={ 1,1 } under multiplication, and define :GG by ([ abcd ])=adbc. Assume that is an epimorphism, and find the elements of K= ker . Write out the distinct elements of G/K. Let :G/KG be the isomorphism described in the proof of Theorem 4.27, and write out the values of .
The following set of matrices [ 1001 ], [ 1001 ], [ 0110 ], [ 0110 ] [ i00i ], [ i00i ], [ 0ii0 ], [ 0ii0 ] forms a group H with respect to matrix multiplication. Find an isomorphism from H to the quaternion group. Sec. 3.1,34 Let G be the set of eight elements G={ 1,i,j,k,1,i,j,k } with identity element 1 and noncommutative multiplication given by (1)2=1, i2=j2=k2=1, ij=ji=k jk=kj=i, ki=ik=j, x=(1)x=x(1) for all x in G (The circular order of multiplication is indicated by the diagram in Figure 3.8.) Given that G is a group of order 8, write out the multiplication table for G. This group is known as the quaternion group.
11. Find two nonzero matrices and such that.
17. Consider the set of matrices, where , , , , Show that is s subgroup of , the general linear group of order over .

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IF P= DF-CB find the value of the following ANS ANS 1 P11 6 P23 2 P12 7 P31 %3D %3D 3. P13 8 P32 %3D %3D 4 21 9 P33 %3D P22 %3D II