2. B >) Given the matrices:(i) Compute det (45):(ii) Compute det (C100) - det(C99):0 -3 300 -3A =-----6=B=3 03 3 01 013 0 -3 C= 15 027 0 1

Answered: Image /qna-images/answer/5d7b3239-24c3-41f4-981e-a99d18635d20.jpg

Answered: >) Given the matrices: (i) Compute det…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.2: Diagonalization

Problem 39E: Are the two matrices similar? If so, find a matrix P such that B=P1AP. A=[100020003]B=[300020001]

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Are the two matrices similar? If so, find a matrix P such that B=P1AP. A=[100020003]B=[300020001]
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 .
In a previous section, we showed that matrix multiplication is not commutative, that is, ABBA in most cases. Can you explain why matrix multiplication is commutative for matrix inverses, that is, A1A=AA1 ?

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>) Given the matrices: (i) Compute det (45): (ii) Compute det (C100) - det (C99): 0 -3 3 3 0 -3 3 3 0 0 -3 ^-[7]---| 3], A = = B = 3 0 C= [0 1 01 15 0 2 7 0 1