\fa. Is the origin an attractor, a repeller, or a saddle point of the dynamical system xk+1 =Axk? An attractor x A repeller * A saddle point b. Find the directions of greatest attraction and/or repulsion for this dynamical system. What is the direction of greatest attraction, if there is one? Select the correct choice below and, if necessary, ll in the answer box to complete your choice. .A, V The direction of greatest attraction is the line through 0 and 1 (Type an integer or decimal for each matrix element.) B. All solutions except the constant zero solution are unbounded and tend away from the origin. There is no direction of greatest attraction. What is the direction of greatest repulsion, if there is one? Select the correct choice below and, if necessary, ll in the answer box to complete your choice. * A. The direction of greatest repulsion is the line through 0 and (Type an integer or decimal for each matrix element.) 'x B. All solutions tend toward the origin. There is no direction of greatest repulsion. c. Make a graphical representation of the system, showing the directions of greatest attraction or repulsion. Include a rough sketch of several typical trajectories (without computing specic points). Choose the correct graph below. *A. X B. c. D. x2 Q x2 a x2 Q x2 Q Q Q E E E