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Does there exist an 8 x 8 matrix A = (as) satisfying the ? hen aj = 0 (a1s denotes the entry in the first row and eighth column of gonalizable exists, provide an example of one and prove that it satisfies . If no such matrix exists, prove that no such matrix exists

Does there exist an 8 x 8 matrix A = (as) satisfying the ? hen aj = 0 (a1s denotes the entry in the first row and eighth column of gonalizable exists, provide an example of one and prove that it satisfies . If no such matrix exists, prove that no such matrix exists

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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» Does there exist an 8 x 8 matrix A = (ais) satisfying the following three conditions? (i) If i > j then aj = 0 (ii) a1s #0 (a18 denotes the entry in the first row and eighth column of A) (iii) A is diagonalizable If such a matrix exists, provide an example of one and prove that it satisfies the given three conditions. If no such matrix exists, prove that no such matrix exists.
Transcribed Image Text:» Does there exist an 8 x 8 matrix A = (ais) satisfying the following three conditions? (i) If i > j then aj = 0 (ii) a1s #0 (a18 denotes the entry in the first row and eighth column of A) (iii) A is diagonalizable If such a matrix exists, provide an example of one and prove that it satisfies the given three conditions. If no such matrix exists, prove that no such matrix exists.
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