4.(i) Consider the 3 x 3 permutation matrix0 1 0P = |0 01 0 0Find all 3 x 3 matrices A such that PAPT = A.%3D(ii) Consider the 4 × 4 permutation matrix0 1 0 00 0 1 00 0 0 11 0 0 0,P =Find all 4 x 4 matrices A such that PAPT = A.

Answered: Image /qna-images/answer/fbc08fad-2592-4124-abc4-e30bd1ff511b.jpg

4. (i) Consider the 3 x 3 permutation matrix 0 1 0 0 0 1 1 0 0 P = Find all 3 x 3 matrices A such that PAPT = A. %3D (ii) Consider the 4 x 4 permutation matrix 0 10 0 0 0 1 0 0 0 0 1 1 0 0 0 P = Find all 4 x 4 matrices A such that PAPT = A. %3D

4. (i) Consider the 3 x 3 permutation matrix 0 1 0 0 0 1 1 0 0 P = Find all 3 x 3 matrices A such that PAPT = A. %3D (ii) Consider the 4 x 4 permutation matrix 0 10 0 0 0 1 0 0 0 0 1 1 0 0 0 P = Find all 4 x 4 matrices A such that PAPT = A. %3D

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.CR: Review Exercises

Problem 64CR: a Find a symmetric matrix B such that B2=A for A=[2112] b Generalize the result of part a by proving...

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Question

4.
(i) Consider the 3 x 3 permutation matrix
0 1 0
P = |0 0
1 0 0
Find all 3 x 3 matrices A such that PAPT = A.
%3D
(ii) Consider the 4 × 4 permutation matrix
0 1 0 0
0 0 1 0
0 0 0 1
1 0 0 0,
P =
Find all 4 x 4 matrices A such that PAPT = A.

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