申論題

4. Let M_n is the nxn matrix with 3's on the main diagonal except the first entry which is 1, 1's directly above the main diagonal and (-1's directly below the main diagonal, and O's elsewhere. For example, We define D_n = det(M_n). Please (a) Find D₁, and D₂, (b) If n ≥ 3, find a formula for D_n in terms of, (c) Find a formula for D_n in terms of n. (15%)