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Question Number 189254 by yaslm last updated on 13/Mar/23

Answered by manxsol last updated on 14/Mar/23

$$\left|\begin{array}{ccccccc}a& 1& 1& 1& 1& 1& 1\\ 1& a& 1& 1& 1& 1& 1\\ & & a& & & & 1\\ & & & .& & & \\ 1& 1& 1& 1& a& 1& 1\\ 1& 1& 1& 1& 1& a& 1\\ 1& 1& 1& 1& 1& 1& a\end{array}\right|$$$$-fn+f_{n-1}$$$$-fn+f_{n-2}$$$$.$$$$-f_n+f1$$$$$$$$\left|\begin{array}{ccccccc}a-1& 0& 0& 0& 0& 0& 1-a\\ 0& a-1& 0& 0& 0& 0& 1-a\\ 0& & a-1& & & & 1-a\\ & & & .& & & \\ 0& 0& 0& 0& a-1& 0& 1-a\\ 0& 0& 0& 0& 0& a-1& 1-a\\ 1& 1& 1& 1& 1& 1& a\end{array}\right|$$$$\left|\begin{array}{ccccccc}a-1& 0& 0& 0& 0& 0& 0\\ 0& a-1& 0& 0& 0& 0& 0\\ 0& & a-1& & & & 0\\ & & & .& & & \\ 0& 0& 0& 0& a-1& 0& 0\\ 0& 0& 0& 0& 0& a-1& 0\\ 1& 1& 1& 1& 1& 1& a+n-1\end{array}\right|$$$$c_1+c_n$$$$c_2+c_n$$$$..$$$$c_{n-1}+c$$$$triangularsuperior$$$$D={(a-1)}^{n-1}(a+n-1)$$$$aplication$$$$a=3$$$$D=2^{n-1}(2+n)$$

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