Question

Find the general solution of the system x' = Ax where A is the given matrix. If an initial condition is given, also find the solution that satisfies the condition. 1.1 5 2 :| -2 1 )

Answer 1

der (A-1)=0 75 21-0 + (9-)(1-1) +4 = 0 x² - 6x +9=0 * (-3) = 0 to the repeated eigenvalues are 1=3 and 22=3 13 (4-)K=0 4 (33)0) = (2)~13 30) = (3) ^ ( )= () so, kitk=0 3 4 24 x=(1) kg -ky This gives an eigen vector and a corresponding solution vector ka (') , *. =(1) to*(A ->22)p=K 712 3)) = 6,1) -15 3)(*)=(7) ~66 0) (16=(**) So, Pet P2 = -% > pi=-1-f2 let pacote then Pr = 4+2 = -2 This gives air ergen vector P = (-44) and a cereresponding solution vector X2 = (41)+ + . The general solution is x=ckett to (kteket Apert) in te, x = 01 () ***}{*)te* +63 ) ess] CScanned with CamScanner