1. The problem statement, all variables and given/known data Draw the phase portrait and classify the origin of the system: xdot = [1 2; 2 1]x 2. Relevant equations characteristic equation: det(A-lambda*I) = 0 3. The attempt at a solution First find the eigenvalues and eigenvectors: det(A-lambda*I) = (lambda+1)(lambda-3) = 0 we can see that the eigenvalues are: lambda_1 = -1 and lambda_2 = 3 for lambda_1 = -1: 2*k1 + 2*k2 = 0 k1 = -k2 when k1 = 1, k2 = - 1 the related eigenvector is (1; -1) for lambda_2 = 3: -2*k1 + 2*k2 = 0 k1 = k2 when k1 = 1, k2 = 1 the eigenvector is K2 = (1; 1) since the matrix of coefficeints is a 2x2 matrix and since we found two linearly independent solutions, the general solution of the system is: X = c1*X1 + c2*X2 = c1*(1;-1)*exp(-t) + c2*(1; 1)*exp(t) or x = c1*exp(-t) + c2*exp(t) y = -c1*exp(-t) + c2*exp(t) We can classify the origin as neither a repeller nor an attractor. Is this correct? Also I feel like I need to provide more information when classifying the origin but I don't know what. For instance should I call the origin a saddle point because it has eigenvalues of different polarities?