+0  
 
0
50
2
avatar

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
 #1
avatar+9457 
0

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
avatar
+1

Oh itś 0 thank you so much!

Guest May 14, 2022

5 Online Users

avatar