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Determinants, Cofactors and Permutations

Q1.
Suppose An is the n by n tridiagonal matrix with 1's everywhere on the three diagonals...

Let Dn be the determinant of An; we want to find it.
(a) Expand in cofactors along the first row of An to show that Dn = Dn-1 - Dn-2

(b) Starting from D1 = 1 and D2 = 0 find D3, D4, ..., D8. By noticing how these numbers cycle around (with what period?) find D1000.

Q2.
Suppose the permutation S takes (1,2,3,4,5) to (5,4,3,2,1).
(a) What does S2 do to (1,2,3,4,5)?

(b) What does S-1 do to (1,2,3,4,5)?

Please see attached for full question.

Gilbert Strang's Linear Algebra and its Applications, 3rd edition.

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Solution Summary

Determinants, cofactors and permutations are investigated. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.

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