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# The Fibonacci sequence is defined by , , for all

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The Fibonacci sequence is defined by $$F_0 = 0,$$$$F_1 = 1,$$$$F_n = F_{n - 1} + F_{n - 2}$$ for all $$n \ge 2.$$

$$\det \begin{pmatrix} F_{1000} & F_{1001} & F_{1002} \\ F_{1001} & F_{1002} & F_{1003} \\ F_{1002} & F_{1003} & F_{1004} \end{pmatrix} .$$ (its not -4)

May 14, 2022

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Note that the third row is just the first row plus the second row.

Doing row operation yields $$\det \begin{pmatrix} F_{1000} & F_{1001} & F_{1002} \\ F_{1001} & F_{1002} & F_{1003} \\ F_{1002} & F_{1003} & F_{1004} \end{pmatrix}=\det \begin{pmatrix} F_{1000} & F_{1001} & F_{1002} \\ F_{1001} & F_{1002} & F_{1003} \\ 0&0&0 \end{pmatrix}$$.

The answer is now obvious if you are familiar with the properties of determinant.

May 14, 2022
#2
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Oh itś 0 thank you so much!

Guest May 14, 2022