Question: Suppose that Show that e At = I cos 2t + 1/2 Asin 2t . Apply this fact to find a general solution of x'

Suppose that

Show that e^At = I cos 2t + 1/2 Asin 2t . Apply this fact to find a general solution of x' = Ax, and verify that it is equivalent to the solution found by the eigenvalue method.

-[- A = 0 -2 2 20 0

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In order to demonstrate that cos2 1 2 sin2 e We can apply the matrix exponentials Taylor series expansion at Icos2t 2 1 Asin2t 0 Let e k 0 k At k Lets ... View full answer

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