Fibonacci sequence - the matrix approach

Question

Question:

Fibonacci Sequence - the matrix approach

The Fibonacci sequence is defined recursively as ƒn+1 = ƒ_n+f_n-1,n>3 with ƒ1 = 1 and ƒ = 2 .

Obtain a closed form formulas for f_n using the iteration matrix   (0,1) applied to the vector [ƒn-1,ƒn]^T.
                                                                                                    (1,1)

Hint: Consider a similarity transform to diagonalize the iteration matrix.