In Exercises 9–14, classify the origin as an attractor, repeller, or saddle point of the dynamical system Find the directions of greatest attraction and/or repulsion.

Solution 14EStep 1 Consider the following dynamical system: , where .To find the solution for the equation , first find the Eigen values of are the corresponding eigenvectors.Compute the characteristic polynomial of the matrix : The roots of the characteristic polynomial are the Eigen values of the matrix .