Question

Let Mn be the nxn matrix that has 2’s along the main diagonal, 3’s directly above the main diagonal, 1’s directly below the main diagonal and 0’s elsewhere.

Let dn = det[Mn]. Clearly, d1 = 2 and d2 = 1.

(a) Use Laplace expansions to find an expression for dn in terms of dn-1 and dn-2. (This expression will be valid for all integers n > 2).