Linear algebra proof of Binet's formula for Fibonacci numbers.
Fibonacci numbers satisfy
$\begin{pmatrix} 1 & 1 \\ 1 & 0 \end{pmatrix}^{n} = \begin{pmatrix} F_{n+1} & F_{n} \\ F_{n} & F_{n-1} \end{pmatrix}$
Diagonalize the matrix on left.
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