Let p be a prime number, let F, denote the field of p elements, and let A be the following 3 x 3 matrix over F,: 0 0 -1 A = 1 0 1 1 (i) Show that the characteristic polynomial of A factorizes as a product of linear factors. (ii) Find the Jordan Canonical Form of A (the answer will depend on p).

Let p be a prime number, let F, denote the field of p elements, and let A be the following 3 x 3 matrix over F,: 0 0 -1 A = 1 0 1 1 (i) Show that the characteristic polynomial of A factorizes as a product of linear factors. (ii) Find the Jordan Canonical Form of A (the answer will depend on p).

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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