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6. [10] For any positive integer n, we define a n x n matrix ab2 bn C2 (2 Dn= : Cn an . where an,..., an are non-zero re
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6. [10] For any positive integer n, we define a n x n matrix ab2 bn C2 (2 Dn= : Cn an . where an,..., an are non-zero real numbers, and b2, ... bn, C2, ..., en aı are real numbers. Notice that for any 1 <i, j<n, we have ali if i = j, b; if i = 1 and j > 2, [Dnlij if i > 2 and j = 1, 0 otherwise. Here [Dnlij is the (i, j)-th component of the matrix Dn. Compute det(Dn). Your answer should depend on n, ai, b; and ci.