Exercise 1. Consider the initial value problem u' Au with initial condition u (0) = uo, where 0. A = A. Find the exponential solutions to u'= Au B. Write down the general solution u (t). C. Prove that for any initial value uo, the magnitude of the solution is invariant in time: |u (1)||² = || uo|| for all f. D. Find u (t) when the initial value is uo = 1 21.

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