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 Am = 0. Verify that

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


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

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