- #1
dracolnyte
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Homework Statement
An n x n array Hn = (hij) is said to be a jacobi matrix if hij = 0 whenever |i - j| >= 2. Suppose Hn also has the property that for each index i, hii = a, hi, i+1 = b and hi,i-1 = c. For instance, H4 =
a b 0 0
c a b 0
0 c a b
0 0 c a
(i) Show that det Hn = a (det Hn-1) - bc (det Hn-2) for n = 3,4,...
(ii) Find det H6.
The Attempt at a Solution
I was thinking of converting this into an upper triangle and use that theorem to solve by finding the product of the main diagonals. but I don't know how to prove for general n x n case and I don't know what it means by det Hn-1 and Hn-2