Mathematical Econ

1) Question. Surmise the two dimensional non-linear continuous dynamical system [#]-[ =(2+0)' ]. Set each constituting equation's righthand side equal to zero (i.e. define its fixed points) and simultaneously solve for r and y; observe that (r, y) = (0, 0) is also a solution. 2) Question. Compute the above system's Jacobian matrix and, adopting (x, y) = (0, 0) , its characteristic polynomial too, finding its eigenvalues through the correspondence of its determinant to zero. 3) Question. Elaborate said characteristic polynomial's eigenvectors, via (J -X1, 2/) v1, 2 = 0, remarking that v1, 2 = 0 1 , 2 B1 , 2 , by which a = 0 # 8 = 1 and 8 = 0 => a = 1. Treat the augmented matrix as J (X1, 2) on its lefthand side and as the zero vector on its righthand counterpart: perform only one Gauss Jordan elimination iteration, so that only one row present a one and a zero, and subsequently write out the row equation in terms of a and S, giving rise to the eigenvector through the above implications. 4) Question. Express such system's general solution under this form: Aged2tv2. In other words, plug in the eigenvalues and eigenvectors computed afore