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.
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.
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.