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Exercise 19

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Fn=∣1−11−11−1…110101…011010…001101…......…∣F_{n}=\begin{vmatrix}1&-1&1&-1&1&-1&\ldots\\ 1&1&0&1&0&1&\ldots\\ 0&1&1&0&1&0&\ldots\\ 0&0&1&1&0&1&\ldots\\ .&.&.&.&.&.&\ldots\end{vmatrix}

where FnF_{n} is the nn-th term of 1,1,2,3,5,…,x,y,x+y,… 1,1,2,3,5,\dots,x,y,x+y,\ldots\,, the Fibonacci sequence, and the determinant is of order n−1n-1.

Hefferon, Linear Algebra, Determinants, Laplace’s Expansion, Exercise 19

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Adapted from Linear Algebra © 2016 Jim Hefferon. Licensed under CC BY-SA 3.0 US. Source: Linear Algebra. Imported at revision df2262e.