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Find all the eigenvalues

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Please see attachment for full problem description and hint.

The solution of the vector-valued differential equation

dX/dt = AX(t) with X(0) = [a1
a2
a3]

is given by:

X(t) = Exp(tA)X(0) = e^tA(X(0))

Explain how you would compute e^tA, and then find the general solution when:

A = [ 0 1 0
0 0 1
-1 1 1]

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This solution calculates the characteristic of the matrix and finds all its eigenvalues.

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