(3)

Fibonacci found a sequence of integers {0 1 1 2 3 5 8 13 21 34}. This sequence sums the previous two Fibonacci numbers. Start with f[1]=0, f[2]=1. Using the difference equation found in part (a), we can view this as a zero-input (zero-excitation) system with initial conditions.

a) What are the roots (y or Gama) of this system?

b) Find the zero-input response equation

c) Find the 28^th and 31^th Fibonacci numbers with this method, you should show your zero-input response calculation here with MATLAB (or calculator)