Consider the n × n determinantin which each entry on the main diagonal is a 2, each entry...

Consider the n × n determinant

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.

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