Let F be a field, and let A be the following 4 × 4 matrix over F:0 0 -1|0 0 0-1A =1 0 -1 00 1-1Find the characteristic polvnomial of A.(i)(ii) Find the minimal polynomial of A.(iii) For which of the following fields F is A diagonalisable over F:(а) F — C?(B) F = R?() F = F3, the field of 3 elements?Give your reasoning.

Let F be a field, and let A be the following 4 × 4 matrix over F: 0 0 -1 0 0 A = -1 1 0 -1 0 0 1 -1 (i) Find the characteristic polvnomial of A. (ii) Find the minimal polynomial of A. For which of the following fields F is A diagonalisable over F: (iii) (a) F = C? (B) F = R? (7) F = F3, the field of 3 elements? %3| %3D

Let F be a field, and let A be the following 4 × 4 matrix over F: 0 0 -1 0 0 A = -1 1 0 -1 0 0 1 -1 (i) Find the characteristic polvnomial of A. (ii) Find the minimal polynomial of A. For which of the following fields F is A diagonalisable over F: (iii) (a) F = C? (B) F = R? (7) F = F3, the field of 3 elements? %3| %3D

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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