Exercise 4.4
(a) Let F=
0 1
1 1
Use MATLAB to find an invertible matrix P and a diagonal matrix D such that $PDP^{-1} = F$
(b) Use MATLAB to compare $F^{10}$ and $PD^{10}P^{-1}$
(c) Let $f = (1, 1)^T$. Compute $Ff$, $F^2f$, $F^3f$, $F^4f$, $F^5f$. Describe the pattern in your answers.
(d) Given a sequence of numbers (1, 1, 2, 3, 5, 8, 13, ...), where each term is the sum of the previous two, find the 30th term of this sequence. (If you are stuck, read the remark below)