Program Explanation Given information: The system is x ′ = [ 28 50 100 15 33 60 − 15 − 30 − 57 ] x . The Eigen values is given as, λ = − 2 , 3 , 3 Explanation: Consider matrix form of the system of equation as A . A = [ 28 50 100 15 33 60 − 15 − 30 − 57 ] The associated Eigen vector with the matrix A is v = [ a b c ] T . Substitute − 2 for λ in coefficient matrix ( A − λ I ) v = 0 , [ 28 + 2 50 100 15 33 + 2 60 − 15 − 30 − 57 + 2 ] [ a 1 b 1 c 1 ] = [ 0 0 0 ] [ 30 50 100 15 35 60 − 15 − 30 − 55 ] [ a 1 b 1 c 1 ] = [ 0 0 0 ] The scalar equation are shown below, 30 a 1 + 50 b 1 + 100 c 1 = 0 15 a 1 + 35 b 1 + 60 c 1 = 0 − 15 a 1 − 30 b 1 − 55 c 1 = 0 Solve the first equation 30 a 1 + 50 b 1 + 100 c 1 = 0 as shown below 30 a 1 + 50 b 1 + 100 c 1 = 0 c 1 = − 3 a 1 + 5 b 1 10 Substitute − 3 a 1 + 5 b 1 10 for c 1 in equation 15 a 1 + 35 b 1 + 60 c 1 = 0 as, 15 a 1 + 35 b 1 + 60 ( − 3 a 1 + 5 b 1 10 ) = 0 15 a 1 + 35 b 1 − 18 a 1 + 30 b 1 = 0 5 b 1 = 3 a 1 b 1 = 3 5 a 1 Substitute 3 5 a 1 for b 1 in equation − 15 a 1 − 30 b 1 − 55 c 1 = 0 . − 15 a 1 − 30 ( 3 5 a ) 1 − 55 c 1 = 0 = 0 11 c 1 = − 33 5 a 1 c 1 = − 3 5 a 1 Consider k as a 1 then the value of b 1 and c 1 can be obtained as, b 1 = 3 5 k and c 1 = − 3 5 k Now the vector can be obtained as, [ a 1 b 1 c 1 ] = [ k 3 5 k − 3 5 k ] = [ 5 3 − 3 ] k Therefore, the associated Eigen vector is obtained as: v 1 = [ 5 3 − 3 ] Substitute 3 for λ in coefficient matrix ( A − λ I ) v = 0 , [ 28 − 3 50 100 15 33 − 3 60 − 15 − 30 − 57 − 3 ] [ a 2 b 2 c 2 ] = [ 0 0 0 ] [ 25 50 100 15 30 60 − 15 − 30 − 60 ] [ a 2 b 2 c 2 ] = [

Differential Equations: Computing and Modeling (5th Edition), Edwards, Penney & Calvis

5th Edition

ISBN: 9780321816252

Author: C. Henry Edwards, David E. Penney, David Calvis

Publisher: PEARSON

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Chapter 5.5, Problem 24P

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Program Description:Purpose of problem is to obtain the general solution of the system x′=[2850100153360−15−30−57]x .

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Chapter 5.5, Problem 23P

Chapter 5.5, Problem 25P

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Chapter 5 Solutions

Differential Equations: Computing and Modeling (5th Edition), Edwards, Penney & Calvis

Ch. 5.1 - Let A=[2347] and B=[3451]. Find (a) 2A+3B; (b)...Ch. 5.1 - Prob. 2P Ch. 5.1 - Find AB and BA given A=[203415] and B=[137032].Ch. 5.1 - Prob. 4P Ch. 5.1 - Prob. 5P Ch. 5.1 - Prob. 6P Ch. 5.1 - Prob. 7P Ch. 5.1 - Prob. 8P Ch. 5.1 - Prob. 9P Ch. 5.1 - Prob. 10P

Ch. 5.1 - Prob. 11P Ch. 5.1 - Prob. 12P Ch. 5.1 - Prob. 13P Ch. 5.1 - Prob. 14P Ch. 5.1 - Prob. 15P Ch. 5.1 - Prob. 16P Ch. 5.1 - Prob. 17P Ch. 5.1 - Prob. 18P Ch. 5.1 - Prob. 19P Ch. 5.1 - Prob. 20P Ch. 5.1 - Prob. 21P Ch. 5.1 - Prob. 22P Ch. 5.1 - Prob. 23P Ch. 5.1 - Prob. 24P Ch. 5.1 - Prob. 25P Ch. 5.1 - Prob. 26P Ch. 5.1 - Prob. 27P Ch. 5.1 - Prob. 28P Ch. 5.1 - Prob. 29P Ch. 5.1 - Prob. 30P Ch. 5.1 - Prob. 31P Ch. 5.1 - Prob. 32P Ch. 5.1 - Prob. 33P Ch. 5.1 - Prob. 34P Ch. 5.1 - Prob. 35P Ch. 5.1 - Prob. 36P Ch. 5.1 - Prob. 37P Ch. 5.1 - Prob. 38P Ch. 5.1 - Prob. 39P Ch. 5.1 - Prob. 40P Ch. 5.1 - Prob. 41P Ch. 5.1 - Prob. 42P Ch. 5.1 - Prob. 43P Ch. 5.1 - Prob. 44P Ch. 5.1 - Prob. 45P Ch. 5.2 - Prob. 1P Ch. 5.2 - Prob. 2P Ch. 5.2 - Prob. 3P Ch. 5.2 - Prob. 4P Ch. 5.2 - Prob. 5P Ch. 5.2 - Prob. 6P Ch. 5.2 - Prob. 7P Ch. 5.2 - Prob. 8P Ch. 5.2 - Prob. 9P Ch. 5.2 - Prob. 10P Ch. 5.2 - Prob. 11P Ch. 5.2 - Prob. 12P Ch. 5.2 - Prob. 13P Ch. 5.2 - Prob. 14P Ch. 5.2 - Prob. 15P Ch. 5.2 - Prob. 16P Ch. 5.2 - Prob. 17P Ch. 5.2 - Prob. 18P Ch. 5.2 - Prob. 19P Ch. 5.2 - Prob. 20P Ch. 5.2 - Prob. 21P Ch. 5.2 - Prob. 22P Ch. 5.2 - Prob. 23P Ch. 5.2 - Prob. 24P Ch. 5.2 - Prob. 25P Ch. 5.2 - Prob. 26P Ch. 5.2 - Prob. 27P Ch. 5.2 - Prob. 28P Ch. 5.2 - Prob. 29P Ch. 5.2 - Prob. 30P Ch. 5.2 - Prob. 31P Ch. 5.2 - Prob. 32P Ch. 5.2 - Prob. 33P Ch. 5.2 - Prob. 34P Ch. 5.2 - Prob. 35P Ch. 5.2 - Prob. 36P Ch. 5.2 - Prob. 37P Ch. 5.2 - Prob. 38P Ch. 5.2 - Prob. 39P Ch. 5.2 - Prob. 40P Ch. 5.2 - Prob. 41P Ch. 5.2 - Prob. 42P Ch. 5.2 - Prob. 43P Ch. 5.2 - Prob. 44P Ch. 5.2 - Prob. 45P Ch. 5.2 - Prob. 46P Ch. 5.2 - Prob. 47P Ch. 5.2 - Prob. 48P Ch. 5.2 - Prob. 49P Ch. 5.2 - Prob. 50P Ch. 5.3 - Prob. 1P Ch. 5.3 - Prob. 2P Ch. 5.3 - Prob. 3P Ch. 5.3 - Prob. 4P Ch. 5.3 - Prob. 5P Ch. 5.3 - Prob. 6P Ch. 5.3 - Prob. 7P Ch. 5.3 - Prob. 8P Ch. 5.3 - Prob. 9P Ch. 5.3 - Prob. 10P Ch. 5.3 - Prob. 11P Ch. 5.3 - Prob. 12P Ch. 5.3 - Prob. 13P Ch. 5.3 - Prob. 14P Ch. 5.3 - Prob. 15P Ch. 5.3 - Prob. 16P Ch. 5.3 - Prob. 17P Ch. 5.3 - Prob. 18P Ch. 5.3 - Prob. 19P Ch. 5.3 - Prob. 20P Ch. 5.3 - Prob. 21P Ch. 5.3 - Prob. 22P Ch. 5.3 - Prob. 23P Ch. 5.3 - Prob. 24P Ch. 5.3 - Prob. 25P Ch. 5.3 - Prob. 26P Ch. 5.3 - Prob. 27P Ch. 5.3 - Prob. 28P Ch. 5.3 - Prob. 29P Ch. 5.3 - Prob. 30P Ch. 5.3 - Prob. 31P Ch. 5.3 - Prob. 32P Ch. 5.3 - Prob. 33P Ch. 5.3 - Verify Eq. 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Knowledge Booster

Program Description: Purpose of problem is to obtain the general solution of the system x ′ = [ 28 50 100 15 33 60 − 15 − 30 − 57 ] x .

Solution Summary: The author explains that the problem is to obtain the general solution of the system of equation as A. The Eigen values are given as, =-2,3,3.

Program Description:Purpose of problem is to obtain the general solution of the system x′=[2850100153360−15−30−57]x .

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Chapter 5 Solutions