Against n , or other positive powers 1.6 exercises exercise 1.1 without calculating the characteristic polynomial of a, de- termine which of ? 0, 1, 2, 3 are eigenvalues of the matrix exercise 1.2 find all equilibrium points of the dynamical system with tran sition matrix 2 -1 0 exercise 1.3 referring to the migration problem between vancouver and richmond, find exact formulas for and the initial conditions are 300 and ro 100, as in the text exercise 1.4 repeat the analysis of the fibonacci system, but assume that every adult pair of rabbits produces 2 pairs of offspring initial condition is the same: 1 juvenile pair.) in particular, find exact for mulas for jn and an, find lim, ao ^n a every month. (the exercise 1.5 solve the 2 x 2 dynamical system 53 this means to find the formulas for n and yn in terms of n exercise 1.6 find the general solution of the dynamical system 37 10 15 12 and sketch the phase portrait. what initial conditions will prevent the system from growing beyond all bounds? exercise 1.7 find a formula for (i)the n-th power of the transition matrix of the fibonacci system.