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matrices is an equivalence relati

matrices is an equivalence relati

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Recall that similarity of matrices is an equivalence relation, that is, the relation is reflexive, symmetric and transitive. 3 -5 is similar to itself by finding an R such that R¹ AR = A. 3 -3 (Reflexivity) Verify that A = 8 4 R We know that A is similar to B = (Symmetry) Verify that B 13 1 since P-¹AP = B where P = T ~ A by finding an Ssuch that S-¹BS = A. We also know that B is similar to C = -18 30 - 11 18 (Transitivity) Verify that A ~ C by finding a T such that T-¹AT = C. 31 Ba since Q¹BQ = C where Q = 2 -3 [23] -2
Transcribed Image Text:Recall that similarity of matrices is an equivalence relation, that is, the relation is reflexive, symmetric and transitive. 3 -5 is similar to itself by finding an R such that R¹ AR = A. 3 -3 (Reflexivity) Verify that A = 8 4 R We know that A is similar to B = (Symmetry) Verify that B 13 1 since P-¹AP = B where P = T ~ A by finding an Ssuch that S-¹BS = A. We also know that B is similar to C = -18 30 - 11 18 (Transitivity) Verify that A ~ C by finding a T such that T-¹AT = C. 31 Ba since Q¹BQ = C where Q = 2 -3 [23] -2
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