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, Does there exist an 8 x 8 matrix A = (as) satisfying the following three conditions? (i) If i 2 j then aj = 0 (ii) a1s # 0 (a1s 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.

, Does there exist an 8 x 8 matrix A = (as) satisfying the following three conditions? (i) If i 2 j then aj = 0 (ii) a1s # 0 (a1s 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.

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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