Question

24. -3 = x 2 2 ANSWER

Answer 1

X' a 2 Here A= 3 5/2 5/2 2 1 • Eigenvalue: The chanceteristic equation of motoix Ais given by, IA-AI1 = 0 돌 1-3-1 2-d 1-3-4 2.5 co 1-2-5 2-X (-3-1) (2-1) + 6.25 - 0 dat & +0.29=0 (140.5) (4+0.) zo do -0.5, -0.5 - Eigenvalues ! -0.5, -0.5 ( Rencato d) • Eigen vectos: AI 2-5 1-2.9 2 3 2.5 -2.5 2 + 0.5o 0 0.5 (252 -2.5 2.5 -2.5 2.5. Now, xduce this matrix R,< R,:(25)

[o a (91053) [:] [:]11:18] acto c etx R₂ < R₂ + 2.5R, The system associated with the eigenvalue A=-0.5 -) 1, X2-0 X, 2x2 Eigen vector codespond to t= -0.5, let X₂ = 1 The q enesal solution for teneated roots is given by, V + Ce ett (w+tu) +cq6+054 (w+tu) 22 X V- [1] -0.54 CH) - [*]*sen lo x, CH= e 0.57 (w+tv) ; CH = -0.50 -0.5t (wtv) + e*O:st Cu x 64 = 2 0:54 (-0.5W-0.stu + v) - 0

Now, Axce-0.5+ (Aw + tAu) -@ composing o & , urget Aw= -0.5W4v Au= -0.50 :] Now, Putu [i] in Aw=-0.5w+v ie. v= Aw+ 0.5W = V (A +0.51) w F-2.5 2.51 -2-5 2.5 [*] where wa w LW, je -2.5 2.5 -2.5 2-5 Pextorm RIR, & R₂+2-5R, R, -2-5 - 1 ] wi-W₂ -0-4 2,-0.htW2 is free canable. Here we let w220. [ Put wingenesul solution, [os] -].[] posts = e, e*** [1]<<<**f*[:]-[] Ontwz Wz

This is required genesel of the given system of equation, At too, b ) lim xets = lim ciec **[:] of C, e cost *{* (11739 2-6S 2) = lim x-) 60 [ ca (6,-0.4) eroist + Czteroost ce-ost +te ost Cice So, Astyo, the solution tends to zero.
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