N1: (a)

  [  2^(-1/2)    - 2^(-1/2) ]
  [                         ]
  [  2^(-1/2)      2^(-1/2) ]

 (b)

  [ 2^(1/2)   - 2^(-1/2)  ]
  [                       ]
  [ 2^(1/2)         0     ]

N2:  [ 2  1]  , no
     [ 4  2]


N3: Unprintable

N4: 4

N5: This question is somewhat ambiguous -- the following answer is
under the assumption that: a) Flies born in the kitchen during a
given hour can't die the same hour b) Flies born in the kitchen during
a given hour don't leave the kitchen that same hour.  Other
assumptions lead to different answers.

Ans: The population does not stabilize, but eventually grows
exponentially, the population becoming arbitrarily large.  The rate of
growth, per hour, is eventually about 1.02302 (a 2.3% increase per
hour), and the limiting ratios can be read off from the fact that
(Bed, Kit, Living) are becomes close to a multiple of the eigenvector
(0.520226, 0.700854, 0.488024).

N6: The bird population increases without bound, with the rate of
increase eventually becoming about 61% a year.  The relative
proportions of the 3 age classes are the same as the eigenvector
(26.1803, 8.09017, 1).  In order to support social security in the
long run, each non-retired bird must pay $2.91/year.