Consider the relationship between two nations, X and Y, and let x(t) and y(t) be their respective armament (i.e. military, weapons, and equipment). In the event of conflict the rate of change of armament for each country with respect to time can be modeled using: x' = ky -alpha x + g y' = lx - beta + h Assume k = 0.35, l = 0.4 alpha = 0.3, Beta = 0.55, g = h = 0 and x(0) = 100 y(0) = 90. A) Write this system of differential equations in matrix form i.e. [x' y'] = A [x y] where A is a matrix of coefficients. b) Find the solutions to this system of differential equations. c) Plot the solutions from b) on the same graph in MATLAB (include your code). Comment on any similarities or differences in the solutions. d) Find the maximum armament for country X