Part 2 (10 points, non-coding task)
The recursive equation that defines the sequence in this problem can be written in a matrix form:
\begin{bmatrix}
F_n \\
F_{n-1}
\end{bmatrix}
= \mathbf{A}
\begin{bmatrix}
F_{n-1} \\
F_{n-2}
\end{bmatrix}, \ \forall \ n \geq 2 ,
where \mathbf{A} \in \Bbb R^{2 \times 2}.
Compute \mathbf{A}.
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Reasoning is not required.
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The value of each entry in \mathbf{A} must be exact. For instance, the following values are exact: \sqrt{3}, \frac{2}{\sqrt{7}}, \pi + \frac{3}{8}, e^2, \sin 40^\circ, \log 18. However, their float approximations are not exact.