Explanation Approach: The unique fundamental matrix for x ′ = A x that satisfies X ( 0 ) = I n is called the transition matrix for x ′ = A x based at t = 0 , and it is denoted by X 0 ( t ) . Calculations: Let A be a n × n matrix and X ( t ) be the fundamental matrix for x ′ = A x . Then, e A t = X ( t ) X − 1 ( 0 ) … ( 1 ) Also, e A t = I n + A t + 1 2 ! A t 2 + ⋯ … ( 2 ) Substitute 0 for t in equation ( 2 ) .

Differential Equations and Linear Algebra (4th Edition)

4th Edition

ISBN: 9780321964670

Author: Stephen W. Goode, Scott A. Annin

Publisher: PEARSON

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Chapter 9.8, Problem 1P

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The transition matrix based at t=0 is given by X0=X(t)X−1(0).

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Differential Equations and Linear Algebra (4th Edition)

Ch. 9.1 - For Question a-j, decide if the given statement is...Ch. 9.1 - For Question a-j, decide if the given statement is...Ch. 9.1 - For Question a-j, decide if the given statement is...Ch. 9.1 - For Question a-j, decide if the given statement is...Ch. 9.1 - Prob. 5TFR Ch. 9.1 - For Question a-j, decide if the given statement is...Ch. 9.1 - Prob. 7TFR Ch. 9.1 - For Question a-j, decide if the given statement is...Ch. 9.1 - Prob. 9TFR Ch. 9.1 - Prob. 10TFR

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