Program Explanation Given information: The coefficient matrix A for homogeneous system x ′ = A x is written below. A = [ 2 3 4 0 1 3 0 0 1 ] Explanation: The characteristics equation for the matrix A is written as, | 2 − λ 3 4 0 1 − λ 3 0 0 1 − λ | = 0 ( 1 − λ ) 2 ( 2 − λ ) = 0 λ 1 = 2 and λ 2 , 3 = 1 Therefore, the eigenvalues are 1 and 2 with multiplicity of 2 and 1, respectively. λ 1 = 2 ⇒ { u 1 = [ 1 0 0 ] T λ 2 , 3 = 1 ⇒ { u 2 = [ 3 − 1 0 ] T u 3 = [ 1 4 − 1 ] T Therefore, the fundamental matrix for the given system is written as, Φ ( t ) = [ e λ 1 t ( u 1 ) e λ 2 t ( u 2 ) e λ 3 t ( u 3 + ( A − λ 3 I ) u 3 t ) ] = [ e 2 t ( 1 ) e t ( 3 ) e t ( 1 + 9 t ) e 2 t ( 0 ) e 3 t ( − 1 ) e t ( 4 − 3 t ) e 2 t ( 0 ) e t ( 0 ) e t

5th Edition

ISBN: 9780135962176

Author: Edwards

Publisher: PEARSON CO

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Problems on Growing Functions

For a given set of functions f and g, the growth of functions states that the function g grows as fast as the function f. The growth rate of algorithms helps determine the algorithm's efficiency and compare its performance to other algorithms.

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Chapter 5.6, Problem 37P

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Program Description: Purpose of the problem is to evaluate eAt .

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Chapter 5.6, Problem 36P

Chapter 5.6, Problem 38P

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Chapter 5 Solutions

EP DIFFERENTIAL EQUATIONS+..-MYLAB ACCE

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 the problem is to evaluate e A t .

Solution Summary: The author explains that the coefficient matrix A for homogeneous system xprime=Ax is written below.

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Program Description: Purpose of the problem is to evaluate eAt .

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Chapter 5 Solutions