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Problem 1: Let 63: e2t 6 X6) = [ 4134: 2: a) Verify that X[t) satises the differential equation XI = [ 4 _2 l

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Problem 1: Let 63: e2t 6 X6) = [ 4134: 2: a) Verify that X[t) satises the differential equation XI = [ 4 _2 l X. b) Find f; X[t) cit. Problem 2: Let V be the set of solutions to the system 1 0 0 1 as": 2 1 2 93+ 0 ed, c7l. 3 2 1 0 Is V a vector space with the stande operations of addition and scalar multiplication? Problem 3: Determine whether the members of the following given set of vectors are linearly independent for 00

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