Answered: 9.21. The characteristic polynomial of…

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9.21. The characteristic polynomial of a matrix A is p(2) = 2²-1-6. Find det (A³), Tr (A³), det (-A-¹) and Tr (-A-¹).

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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Question

I'm currently struggling to solve this problem using matrix notation exclusively, and I'm looking for your help. The problem specifically requires a solution using matrix notation alone, without any other methods. Could you please provide a step-by-step explanation in matrix notation to guide me towards the final solution?

i haveb provided the question and answer

Find Tr(-2A) and det (-2A-¹).
9.21. The characteristic polynomial of a matrix A is p(a) = 2² - 2 - 6. Find
det (A³), Tr (A³), det (-A-¹) and Tr (-A¯¹).
9.22 Let 4 he an
matrix and let P ho an invertible my
matriy Show

9.21 det (4³) = -216, Tr (4³) = 19, Tr (-4-¹) = det (-4-¹) = -

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