- Problem 4
Show that the characteristic equation of the matrix is as stated, that is,
is the polynomial associated with the relation.
(Hint: expanding down the final column, and using induction will work.)
- Problem 5
Given a homogeneous linear recurrence relation
, let , ..., be the
roots of the associated polynomial.
- Prove that each function
satisfies the recurrence (without initial conditions).
- Prove that no is .
- Prove that the set
is linearly independent.
- Problem 6
(This refers to the value
given in the computer code below.)
Transferring one disk per second, how many years would it take
the priests at the Tower of Hanoi to finish the job?