Suppose a 3x3 matrix A admits a factorization as A=PDP-1 where P is some invertible matrix and D is the diagonal matrix shown to the right. Show that this factorization is useful when computing high powers of A. Find fairly simple formulas for A², A³, and AK (k a positive integer), using P and the entries in D.

Suppose a 3x3 matrix A admits a factorization as A=PDP-1 where P is some invertible matrix and D is the diagonal matrix shown to the right. Show that this factorization is useful when computing high powers of A. Find fairly simple formulas for A², A³, and AK (k a positive integer), using P and the entries in D.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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