Question: Construct the general solution of x = Ax involving complex eigenfunctions and then obtain the general real solution. Describe the shapes of typical trajectories. 1

Construct the general solution of x\" = Ax involving complex eigenfunctions and then obtain the general real solution. Describe the shapes of typical trajectories. 1 2 A= 5 10 -6 Lnoose the correct general solution of X' = AX Involving complex eigentuncuons below. 14 52 4t - -4t x(t)=c e +cC 5 e A 1 10 } 2 -6 5+1 5-1 oy 5 5 [5 14t -5 | st e x(t)=c e +cC e O C. 1 5} 2 5 r 52 14+i | (4420 - | a-2it O D. X(t)=c4 1016 +cp 2 e L -6-i What is the general real solution? Re(x(t)) = Describe the shapes of typical trajectories of Re(x(t)). Choose the correct answer below. () The trajectories spiral inward toward from the origin. () The trajectories spiral outward from the origin. () The trajectories form ellipses around the origin

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