A matrix A is said to be nilpotent if there exists some positive integer m such that A m 0 Verify that is nilpotent Discuss why it is relatively easy to compute e At when A is nilpotent Compute e At and then use (1) to solve the system X ' AX 1 1 1 0 1 1 A 1...

Verify that A is nilpotent Therefore A m A 3 0 ie m3 15 Nilpotent Now ...

A matrix A is said to be nilpotent if there exists some positive integer m such that

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A matrix A is said to be nilpotent if there exists some positive integer m such that A^m = 0. Verify that

-1 1 -1 0 -1 1 A = 1

is nilpotent. Discuss why it is relatively easy to compute e^At when A is nilpotent. Compute e^At and then use (1) to solve the system X' = AX.

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A First Course in Differential Equations with Modeling Applications

ISBN: 978-1111827052

10th edition

Authors: Dennis G. Zill

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A matrix A is said to be nilpotent if there exists some positive integer m such that

Question:

-1 1 -1 0 -1 1 A = 1

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Verify that A is nilpotent Therefore A m A 3 0 ie m3 15 Nilpotent Now ...View the full answer

A First Course in Differential Equations with Modeling Applications

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