Plz complete Consider the sequence defined recursively by a₁ =[an-1a. Find a matrix that satisfiesanM=Db. Find the appropriate exponent k such thatan[₂]an+1,P-1= Mkd. Find P-¹.=M5kc. Find a diagonal matrix D and an invertible matrix P such that M = PDP-¹.1.89-e. Find M5 = PD5P-¹.Anan+1_I-M-1, a2 = 2, an+1 = -4an-1 - 5an. We can use matrix diagonalization to find an explicit formula for an.f. Use parts b. and e. to find a6.a6 =g. You can find an explicit formula for an using part b. and a formula for Mk = PDP-¹. Try to develop this formula. Use your formula to verify the answer for part f.

Answered: Image /qna-images/answer/24bd6026-ba03-420b-9fbe-e259357f6c2d.jpg

Consider the sequence defined recursively by a₁ = -1, a2 = 2, an+1 = -4an-1-5an. We can use matrix diagonalization to find an explicit formula for an. an-1 a. Find a matrix that satisfies = M an 188 b. Find the appropriate exponent k such that an = Mk an+1] M = k= c. Find a diagonal matrix D and an invertible matrix P such that M = PDP-¹. 1.88 8-18.8 P = D = d. Find P-1 P-¹ = an [an+1] e. Find M5 PD5 P-1. 188 f. Use parts b. and e. to find aç. M5 = a6 = g. You can find an explicit formula for an using part b. and a formula for M* = PDP-1. Try to develop this formula. Use your formula to verify the answer for part f

Consider the sequence defined recursively by a₁ = -1, a2 = 2, an+1 = -4an-1-5an. We can use matrix diagonalization to find an explicit formula for an. an-1 a. Find a matrix that satisfies = M an 188 b. Find the appropriate exponent k such that an = Mk an+1] M = k= c. Find a diagonal matrix D and an invertible matrix P such that M = PDP-¹. 1.88 8-18.8 P = D = d. Find P-1 P-¹ = an [an+1] e. Find M5 PD5 P-1. 188 f. Use parts b. and e. to find aç. M5 = a6 = g. You can find an explicit formula for an using part b. and a formula for M* = PDP-1. Try to develop this formula. Use your formula to verify the answer for part f

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section: Chapter Questions

Problem 52RE

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