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(VI) (VII) (VIII) integer?) Find A¹07 by writing as linear combination of eigenvectors of A. b Find a formula for Ak for all non-negative integers k. (Can k be a negative Use (VII) to find A¹06 and compare it with what you found in (VI).

(VI) (VII) (VIII) integer?) Find A¹07 by writing as linear combination of eigenvectors of A. b Find a formula for Ak for all non-negative integers k. (Can k be a negative Use (VII) to find A¹06 and compare it with what you found in (VI).

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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Can you please provide a full solution and explanation for this question. Thank you!!

A = -3 4 -2 3 -8 8 1 " B = 1 0 0 0 0 -1 0 0 1 5 = 3
Transcribed Image Text:A = -3 4 -2 3 -8 8 1 " B = 1 0 0 0 0 -1 0 0 1 5 = 3
(VI) (VII) (VIII) (IX) integer?) Find A¹07 by writing b as linear combination of eigenvectors of A. Find a formula for Ak for all non-negative integers k. (Can k be a negative Use (VII) to find A¹⁰ and compare it with what you found in (VI). Is A similar to B? If yes, find an invertible matrix such that P-¹AP = B.
Transcribed Image Text:(VI) (VII) (VIII) (IX) integer?) Find A¹07 by writing b as linear combination of eigenvectors of A. Find a formula for Ak for all non-negative integers k. (Can k be a negative Use (VII) to find A¹⁰ and compare it with what you found in (VI). Is A similar to B? If yes, find an invertible matrix such that P-¹AP = B.
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What about part IX), is A similar to B, I think it is not similar, if I am correct or not please provide an explanation. Thank you!

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