Explanation Given: The given matrix is A= ( 1 1 1 1 1 1 − 2 − 2 − 2 ) . Formula used: For any n × n matrix A , e A t = 1 + A t + A 2 2 ! t 2 + A 3 3 ! t 3 + … + A k k ! t k + … Calculation: Compute A 2 as follows. A 2 = A ⋅ A = ( 1 1 1 1 1 1 − 2 − 2 − 2 ) ⋅ ( 1 1 1 1 1 1 − 2 − 2 − 2 ) = ( 0 0 0 0 0 0 0 0 0 ) Similarly A 3 is calculated by multiplying matrix A 2 with matrix A as follows. A 3 = A 2 ⋅ A = ( 0 0 0 0 0 0 0 0 0 ) Similarly A 4 is calculated by multiplying matrix A 3 with matrix A as follows

A First Course in Differential Equations with Modeling Applications (MindTap Course List)

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ISBN: 9781305965720

Author: Dennis G. Zill

Publisher: Cengage Learning

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Chapter 8.4, Problem 3E

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To find: The value of eAt for the given matrix.

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Chapter 8.4, Problem 2E

Chapter 8.4, Problem 4E

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A First Course in Differential Equations with Modeling Applications (MindTap Course List)

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The value of e A t for the given matrix.

Solution Summary: The author calculates the value of eAt for the given matrix.

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