questions below:

Construct the general solution of x' = Ax involving complex eigenfunctions and then obtain the general real solution. Describe the shapes of typical trajectories. 10 6 A= 3 6 Choose the correct general solution of x' = Ax involving complex eigenfunctions below. O A. C1 2+ i OB. C1 3 eat + 0 2 3 e - 2 10 OC . G 6+ i e (2+ 2i)t + C2 3 e (2-2i)t -2- i 10 OD. C1 e 21 + C2 3 eChoose the correct general real solution below. N 2 O A. C1 e 6t + C2 e - 2t 3 3 2 cos (2t) - sin (2t) 2 sin (2t) + cos (2t) OB. C1 e 2t + C2 e 2t 3 cos (2t) 3 sin (2t) 2 co: cos (2t) - sin (2t) O C. C1 e 2t 3 co: form ellipses around -3 i sin (2t) 6 spiral outward from OD. C1 e 6 spiral inward toward The trajectories the origin.Find a basis for the eigenspace corresponding to each listed eigenvalue. 4 6 A= ,7L=1,2 -1 -1 A basis for the eigenspace corresponding to A = 1 is U. (Type a vector or list of vectors. Type an integer or simplied fraction for each matrix element. Use a comma to separate answers as needed.) A basis for the eigenspace corresponding to A = 2 is {11}. (Type a vector or list of vectors. Type an integer or simplied fraction for each matrix element. Use a comma to separate answers as needed.) Describe what happens to xx as k-co. Choose the correct answer below. O A. As k becomes sufficiently large, Xx ~ 0.5(0.1)k 0 2 2 O B. As k becomes sufficiently large, Xx ~ 0.3(0.7)k -2 + 0.5(0.1)k 0 2 0.1 O C. As k becomes sufficiently large, XK ~ |0.4 0.3