Program Explanation Given information: The vectors for the system of differential equations is, x ′ = [ − 8 − 11 − 2 6 9 2 − 6 − 6 1 ] x ; x 1 = e − 2 t [ 3 − 2 2 ] , x 2 = e t [ 1 − 1 1 ] and x 3 = e 3 t [ 1 − 1 0 ] Explanation: The given vectors for the system of differential equations is, x ′ = [ − 8 − 11 − 2 6 9 2 − 6 − 6 1 ] x ; x 1 = e − 2 t [ 3 − 2 2 ] , x 2 = e t [ 1 − 1 1 ] and x 3 = e 3 t [ 1 − 1 0 ] To verify that the vector functions x 1 and x 2 are solutions of matrix differential function, the vector functions x 1 and x 2 are calculated as, x 1 = [ 3 e − 2 t − 2 e − 2 t 2 e − 2 t ] ⇒ x 1 ′ = [ − 6 e − 2 t 4 e − 2 t − 4 e − 2 t ] x 2 = [ e t − e t e t ] ⇒ x 2 ′ = [ e t − e t e t ] Similarly, the value of vector function x 3 is calculated as, x 3 = [ e 3 t − e 3 t 0 ] ⇒ x 3 ′ = [ e 3 t − e 3 t 0 ] The coefficient matrix P is calculated as, P x 1 = [ − 8 − 11 − 2 6 9 2 − 6 − 6 1 ] [ 3 e − 2 t − 2 e − 2 t 2 e − 2 t ] P x 1 = [ − 6 e − 2 t 4 e − 2 t − 4 e − 2 t ] = x 1 ′ P x 2 = [ − 8 − 11 − 2 6 9

MyLab Math with Pearson eText -- 24-Month Standalone Access Card -- For Differential Equations and Boundary Value Problems: Computing and Modeling Tech Update

5th Edition

ISBN: 9780134872971

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

Publisher: PEARSON

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Chapter 5.1, Problem 29P

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Program Description: Purpose of problem is to write the general solution of the system and verify that the given vectors are solutions of the system. Also, show that they are linearly independent.

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Chapter 5.1, Problem 28P

Chapter 5.1, Problem 30P

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Chapter 5 Solutions

MyLab Math with Pearson eText -- 24-Month Standalone Access Card -- For Differential Equations and Boundary Value Problems: Computing and Modeling Tech Update

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

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Program Description: Purpose of problem is to write the general solution of the system and verify that the given vectors are solutions of the system. Also, show that they are linearly independent.

Solution Summary: The author explains how the vectors for the system of differential equations are linearly independent.

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Program Description: Purpose of problem is to write the general solution of the system and verify that the given vectors are solutions of the system. Also, show that they are linearly independent.

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Chapter 5 Solutions