Math 2602 B1, B2                                                                             Homework  #11
                                       Due Tuesday, November 16, 2004


    1.  (from an old test)  Let (a_n) and (b_n) be the sequences defined by a₀ = 1 and b₀ = 0 , and
                                                                                               2      0
         ( a_n , b_n )^T =  A(a_n-1 , b_n-1) , for n > 1 , where  A =     1   -1/2   .

      a)  Show that 2 and -1/2 are eigenvalues of  A .







     b)  Find a_n and b_n .


























   c)  Determine whether a_n = o(b_n) , b_n = o(a_n) , or neither.