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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 A* (k a positive integer), using P and the entries in D. A² = D= N O O - 00 8

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 A* (k a positive integer), using P and the entries in D. A² = D= N O O - 00 8

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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Suppose a 3x3 matrix A admits a factorization as A=PDP 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 positive integer), using P and the entries in D. 3 (ka A²: = 200 1 0 0 D= 3 00 - 00
Transcribed Image Text:Suppose a 3x3 matrix A admits a factorization as A=PDP 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 positive integer), using P and the entries in D. 3 (ka A²: = 200 1 0 0 D= 3 00 - 00
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