Could you answer these questions? thanks

4. Consider the following linear system x' i _4 w x _ 1 0 with as being a real valued parameter. The system has an equilibrium point at origin x = [0, 0]T. For each of the following types of equilibria, determine the values of w such that the equilibrium at origin is of that type. If there is no such w, state \"None\". (a)IT= (b) The equilibrium is a nodal source. ((2) The equilibrium is a nodal sink. (d) The equilibrium is a spiral source. (e) The equilibrium is a spiral sink. (f) The equilibrium is a saddle point. (g) The equilibrium is a center. (h) For what value of w are all solutions guaranteed to approach the equilibrium at origin as t )- oo