1. For the system r = r2. 12 = -r1, [:] 1 is a complex-valued solution....

 

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1. For the system r = r2. 12 = -r1, [:] 1 is a complex-valued solution. Derive from this solution two linearly inde- pendent real-valued solutions r' (t) and a2(t). 2. Let A, P, and D be nxn matrices, where P is nonsingular and D is diagonal, and such that A = PDP-1, Prove that e4 = PEPP-1. 1. For the system r = r2. 12 = -r1, [:] 1 is a complex-valued solution. Derive from this solution two linearly inde- pendent real-valued solutions r' (t) and a2(t). 2. Let A, P, and D be nxn matrices, where P is nonsingular and D is diagonal, and such that A = PDP-1, Prove that e4 = PEPP-1.