Homework  8  427K-H  due Wednesday April 10
.
1.  Find the general solution to the equation Y' = AY  where A is
the 3x3 matrix [1,2,3;3,0,3;9,2,1].


2.  If X' = AX  give the eigenvalues of A and determine the stability
of the fixed or equilibrium point 0  when:



a) A= [ 1, 0, 2;2,2,0;5,-2, 3].

b) A = 1,0,1,4;4,-1,0,3;3,-4,0,6;1,0,0,10].

c)  A = [1,-3;-2,10]

d) A = [-2,1,0;-5,-1,0; 1,0,3].

3. page 410 #2

4.  page 410  # 17

5.  Consider the non-linear system  

     x' = x(3 - y -2 x)
     y' = y(3 - x -2 y).

Find the fixed points and determine the stability of each fixed point.