001 001

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Find the matrix exponential for the nilpotent matrix?

Find the matrix exponential for the nilpotent matrix

A=
001
001
000

Note: This has been fixed.

Since A =
[0 0 1]
[0 0 1]
[0 0 0], we have

A^2 =
[0 0 0]
[0 0 0]
[0 0 0], and

So, A^k = 0 for all k = 2, 3, 4, 5, ...
-----------------
Therefore, e^A
= I + A + (1/2!) A^2 + (1/3!) A^3 + ...
= I + A + 0 =
[1 0 1]
[0 1 1]
[0 0 1].

I hope this helps!

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