Program Explanation Given information: The vectors for the system of differential equations is, x ′ = [ 3 − 2 0 − 1 3 − 2 0 − 1 3 ] x ; x 1 = e t [ 2 2 1 ] , x 2 = e 3 t [ − 2 0 1 ] and x 3 = e 5 t [ 2 − 2 1 ] Explanation: The given vectors for the system of differential equations is, x ′ = [ 3 − 2 0 − 1 3 − 2 0 − 1 3 ] x ; x 1 = e t [ 2 2 1 ] , x 2 = e 3 t [ − 2 0 1 ] and x 3 = e 5 t [ 2 − 2 1 ] 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 = [ 2 e t 2 e t e t ] ⇒ x 1 ′ = [ 2 e t 2 e t e t ] x 2 = [ − 2 e 3 t 0 e 3 t ] ⇒ x 2 ′ = [ − 6 e 3 t 0 3 e 3 t ] Similarly, the value of vector function x 3 is calculated as, x 3 = [ 2 e 5 t − 2 e 5 t e 5 t ] ⇒ x 3 ′ = [ 10 e 5 t − 10 e 5 t 5 e 5 t ] The coefficient matrix P is calculated as, P x 1 = [ 3 − 2 0 − 1 3 − 2 0 − 1 3 ] [ 2 e t 2 e t e t ] P x 1 = [ 2 e t 2 e t e t ] = x 1 ′ P x 2 = [ 3 − 2 0 − 1 3 − 2 0 − 1 3 ] [ − 2 e 3 t 0 <

5th Edition

ISBN: 9780135904206

Author: Edwards

Publisher: PEARSON

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Linear Programming Concepts

Linear programming is a famous mathematical modeling tool for determining the best distribution of scarce resources among competing demands. Machinery, time, personnel, raw materials, money, and space are all resources. It is used to find the most optima…

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Chapter 5.1, Problem 26P

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Program Description: Purpose of problem is to write the general solution of the system x′=[3−20−13−20−13]x;x1=et[221], x2=e3t[−201] and x3=e5t[2−21] 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 25P

Chapter 5.1, Problem 27P

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Chapter 5 Solutions

DIFFERENTIAL EQUATIONS+..-MYLAB ACCESS

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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Solution Summary: The author explains that the given vectors are solutions of the system, and that they are linearly independent.

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Program Description: Purpose of problem is to write the general solution of the system x′=[3−20−13−20−13]x;x1=et[221], x2=e3t[−201] and x3=e5t[2−21] 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