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Fibonacci Sequence - the matrix approach

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The Fibonacci sequence is defined recursively as f_(n+1) = f_n + f_(n-1) .

Obtain a closed form formulas for f_n using the iteration matrix (0,1,1,1) applied to the vector .. (see attached file). Consider a similar transform to diagonalize the iteration matrix.

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The 5-pages solution shows how to obtain the general closed-form expression for the n'th term of the Fibonacci sequence using a matrix approach.

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The characteristic equation of the matrix is:
(1.1)
Which leads to:

(1.2)
Note that for both eigenvalues:

(1.3)

And:

...

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