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.
Please see the attached file for the complete solution.
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a) It is easy to know that , . Now we consider . We know that for the matrix , , has the following form
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.