For any positive integer n, Bn is a n x n matrix. B is a n x n matrix. n is an arbitrary positive integer. -a -a -a -a ... a -a .. -a -a a a -a -a ... Bn ... a a а -a ... а а a a -a ... In fact, for any 1< i,j < n, [Bn]ij = a if i > j, | [Bn]ij = -a if i < j, [Bn]ij = x if i = j and j < n – 1, |[Bn]ij = -a if i = j = n. Here [Bn]ij is the (i,j)-th entry of the matrix Bn. What is det(Bn)? You need to express det (Bn) as a function depending on n, x and a. You need to give detailed explanation how to obtain your answer.

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