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8. (11 pts) Let (Xn) be a sequence in Rº such that VnEN, Xn+1 = A· Xn+ where A = (5/8 5/3) and Xo = (-1) (a) (1 pt) Find X1.* Xmdi? Axm + (!) theme A ) and * = (-) Where and Xo - @ X2 = A xo + C) 2)61)-(1) G- X© Determine two eigen value of A. het a be the eigen value of A. then, det (A-df2) = 0 - 54 Leo 로 시 > (글) - 5 0 | 3 28 금 + 4point the corresponding equibrium depends on eien value of A. and As the eigen values are real opposite sign. do they are sad2. x,=282 so, put X2=1 :v,= ( x ) = (2) - for d,= 3 we get the eigen rector v=12) is for q = -1/2 let v2 = ( 4 ) be the eigenjust answer e through h

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Answer #1

Ce). For pThree le ye Eilhim pint Cse ores epellar ven by notry A AHA Camili bti um prit is ん Sed fink

Note that, this is given to be a linear map, not a linear first order system of ordinary differential equation.

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