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2. (i) Let x, y be vectors in R?. Can one find a 4 x 4 permutation matrix P such that P(x y) = y ® x? (ii) Let A, B be 2 x 2 matrices. Can one find a 4 x 4 permutation matrix such that P(A® B)P¯1 = B® A? (iii) Consider the vectors u and v in C3 -) --E) u = u2 v = v2 U3 V3 %3D Find the 9 x 9 permutation matrix P such that P(u 8 v) = v ® u.

2. (i) Let x, y be vectors in R?. Can one find a 4 x 4 permutation matrix P such that P(x y) = y ® x? (ii) Let A, B be 2 x 2 matrices. Can one find a 4 x 4 permutation matrix such that P(A® B)P¯1 = B® A? (iii) Consider the vectors u and v in C3 -) --E) u = u2 v = v2 U3 V3 %3D Find the 9 x 9 permutation matrix P such that P(u 8 v) = v ® u.

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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2. (i) Let x, y be vectors in R². Can one find a 4 x 4 permutation matrix P such that P(x ® y) = y ® x? (ii) Let A, B be 2 x 2 matrices. Can one find a 4 x 4 permutation matrix such that P(A® B)P¯1 = B ® A? (iii) Consider the vectors u and v in C3 -) -(6) vi u = u2 v = V2 u3 V3 Find the 9 x 9 permutation matrix P such that P(u 8 v) =
Transcribed Image Text:2. (i) Let x, y be vectors in R². Can one find a 4 x 4 permutation matrix P such that P(x ® y) = y ® x? (ii) Let A, B be 2 x 2 matrices. Can one find a 4 x 4 permutation matrix such that P(A® B)P¯1 = B ® A? (iii) Consider the vectors u and v in C3 -) -(6) vi u = u2 v = V2 u3 V3 Find the 9 x 9 permutation matrix P such that P(u 8 v) =
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