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Consider the permutation matrix P[i,j]er dxd with 1≤i

Consider the permutation matrix P[i,j]er dxd with 1≤i

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Linear Transformations
Section6.4: Transistion Matrices And Similarity
Problem 29E
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dxd Consider the permutation matrix P[i,j]ER with 1<i<j≤d. For which integers KEN do we have P[i,j]K=I, where I denotes the identity matrix? a. This is always true for k=1. b. Whether this is true for k=1 depends on the choice of i and j. c. This is false for k=1. d. e. O f. This is always true for k=2. Whether this is true for k=2 depends on the choice of i and j. This is false for k=2. g. This is always true for k=3. Oh. Whether this is true for k=3 depends on the choice of i and j. Oi. This is false for k=3.
Transcribed Image Text:dxd Consider the permutation matrix P[i,j]ER with 1<i<j≤d. For which integers KEN do we have P[i,j]K=I, where I denotes the identity matrix? a. This is always true for k=1. b. Whether this is true for k=1 depends on the choice of i and j. c. This is false for k=1. d. e. O f. This is always true for k=2. Whether this is true for k=2 depends on the choice of i and j. This is false for k=2. g. This is always true for k=3. Oh. Whether this is true for k=3 depends on the choice of i and j. Oi. This is false for k=3.
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