Given Y = c1e1tx1 + c2e2tx2 + +cnen txn is the solution to the initial value problem: Y_
Chapter 6, Problem 3(choose chapter or problem)
Given Y = c1e1tx1 + c2e2tx2 + +cnen txn is the solution to the initial value problem: Y_ = AY, Y(0) = Y0 (a) Show that Y0 = c1x1 + c2x2 + +cnxn (b) Let X = (x1, . . . , xn) and c = (c1, . . . , cn)T . Assuming that the vectors x1, . . . , xn are linearly independent, show that c = X1Y0.
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