Question: Consider the n x n determinant in which each entry on the main diagonal is a 2, each entry on the two adjacent diagonals is

Consider the n x n determinant


Bn = 2100 2 1 1 1 0 0 2 1 0000


in which each entry on the main diagonal is a 2, each entry on the two adjacent diagonals is a 1, and every other entry is zero.


(a) Expand along the first row to show that Bn = 2Bn-1 - Bn-2.


(b) Prove by induction on n that Bn = n + 1 for n ≥ 2.

Bn = 2100 2 1 1 1 0 0 2 1 0000 0000 00 - 00 0 0 21 12

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