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LLL វ 2] = [5, 3]. 8 Find formulas for the entries of M", where n is a positive integer. M": = M

LLL វ 2] = [5, 3]. 8 Find formulas for the entries of M", where n is a positive integer. M": = M

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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LLL វ 2] = [5, 3]. 8 Find formulas for the entries of M", where n is a positive integer. M": = M
Transcribed Image Text:LLL វ 2] = [5, 3]. 8 Find formulas for the entries of M", where n is a positive integer. M": = M
124 = 27-2² M": = -12 = 2²-24 -120 = 2³-27 6=2³-2 6026-22 -4 = 2²-2³ -56 = 2³ - 26 Step 3 We can see that the larger power of 2 increases by 3 for every 1 that the smaller power of 2 increases by, so we postulate the following formulas: [2³n+1 _ 2n 2³n - 2n 2n+1 _ 23n+1- 2n - 23n
Transcribed Image Text:124 = 27-2² M": = -12 = 2²-24 -120 = 2³-27 6=2³-2 6026-22 -4 = 2²-2³ -56 = 2³ - 26 Step 3 We can see that the larger power of 2 increases by 3 for every 1 that the smaller power of 2 increases by, so we postulate the following formulas: [2³n+1 _ 2n 2³n - 2n 2n+1 _ 23n+1- 2n - 23n
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