Question

Please clear hand write ,thank you ????

5. a) (7 pnts) Determine the general solution to the system x' = Ax for the given matrix A = [2 81 b) (6 pnts) Write one unique solution, by assuming some values for the arbitrary coefficients. c) (7 pnts) Ast → 00, what could you say about the limit of the solutions of this system?

Answer 1

< 1972 0-2 8 2 0-2 (?) E (1-4) (+4) ► Details 1.11 = 4 2.12 = -4 2. For every a we find its own vector(s): 1.17 = 4 -4 8 2 -4 Av = av * (A-AI) v = 0

General Solution : X= (via {azu(3) The solution set: {X2 X III 2 Let x 2 = 1, V1 = 2.12 = -4 A-121 4 8 2 4 २ ) Av = av * (A-2) = 0

General Solution : X = -2x2 X2 The solution set: {X2 faz-(17) X Let x 2 = 1, V2 = -2 1

General solue of the given systemi 3-968 +91973) ( Taking a=22=1 we et the one unique solu? #t/- a(t) = ext (2) 2 .at/ e + Ato the a ne ferm solu will vanished. So will at in the the solut general del x-Gent (3)