+29 The Fibonacci sequence is defined by \(F_0 = 0,,F_1=1\) and \(F_n = F_{n - 1} + F_{n - 2} \) for all \(n \ge 2.\)
Compute \(\det \begin{pmatrix} F_{1000} & F_{1001} & F_{1002} \\ F_{1001} & F_{1002} & F_{1003} \\ F_{1002} & F_{1003} & F_{1004} \end{pmatrix} .\)
