Question

Solve the following I VP x":]xof]

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Answer 1

X 10)= let A = Tofrnd eizen value tA TAdI) =06-A -1 4-A > (6-8)(4-d) +5 -0 2 24-6A-4ad to ts-0 > 2101 +29 =0 10 t 100-4 C29) 2d: lot ToD -116 lot Fic ad= lot 4i %3D d=s +zl d= 5-2i d =S+2é Consider 7-z

-> (1-2) se=X2 (1-2i) u -x2 =0 >-> 5 sep + (-1+2i)H2=0 51 + (-1 +2i) (l-2u)24=0 is -- eigen vector : first solution XIt)= è (st zd) t st COS Cos2t simzt COS 2t +251n2t sint-2 (as Uzet) UCH) 5t 5t so Weget theseution fer complex weneedner to fHnd the solution fer second elgenvelue Wegeh sdme 412 st CUs 2t : XCH) = G eG sin2t-20as2t Cas zt+ 251int

We haue XIt) = -2= X,(0) = Cie coszt t(2esinzt Cie cos 2t + Czèt sinzt %3D + C2x0. CI CUS2E %3D Xect) = é t (cos2tt2ulinzt) 52t- 20052t) C2 ( coso+ 21no) + C2 [Sino - 2G) = C * = 2( = G C1) + (2 (-2) 8 = X2 C0) :(1=-2 %3D -2 )+(2(-2) -2 - 2C2 10 > (2 = -G -212 %3D (Sin2t) St COE XCH) = %3D Sinzt- COS 2t +25in thank you?