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Solve each of the following systems by the eigenvalue method. If ICs are given, find the...

Solve each of the following systems by the eigenvalue method. If ICs are given, find the particular solution to the system. If no ICs are given, find the general solution. Write all solutions in vector form.

x'1 = -2x1 + 5x2, x'2 = -6x1 + 9x2; x1(0) = 1; x2(0) = 3

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