Question

3) Use matrix exponential to solve da = =x2 d22 at -X, X,10)=1, X260)=1

Answer 1

Son 004 drea ry =-* 1,16) = 1 %,(o)=1 ni whore A= X'= AX. - od+1=0 for da eigen vector dat .-)(3)=6) for dai - ix + = 0 = ix, - - ih=0 x = -ex set x = 1, R₂ = Hence v = ( + lote II -1 ixt2 =0 = -ix x = 24 Lot K₂ =- Hence eigen vector .:))-(3) - Mtix=0 M = 1 ) Then -it Siirete X = C + 4(1) = Geit Gelt $ Xa= içeitigelt I= Getge I L=içe ile 1=G+2 i (G-C₂) = 1 i (a +(2) = gig=lti G = 1-2 (g = 1-9 g = 1 - 2 + 2 = £ti Ise teh + 17h ett) = (1-1) eelt • (14) ieet I = e(C-(e) » G=lato G= 1 - 1 i-L. Then

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