一.公式法
a+b a 0 ...0 0
b a+b a ...0 0
0 b a+b ...0 0
.........
0 0 0 ...a+b a
0 0 0 ...b a+b
当a≠b时,Dn = [a^(n+1)-b^(n+1)]/(a-b)
行列式 = 3^6-2^6 = 665.
二.化对角行列式
5 3 0 0 0
2 5 3 0 0
0 2 5 3 0
0 0 2 5 3
0 0 0 2 5
r2-(2/5)r1
5 3 0 0 0
0 19/5 3 0 0
0 2 5 3 0
0 0 2 5 3
0 0 0 2 5
r3-(10/19)r2
5 3 0 0 0
0 19/5 3 0 0
0 0 65/19 3 0
0 0 2 5 3
0 0 0 2 5
r4-(38/65)r3
5 3 0 0 0
0 19/5 3 0 0
0 0 65/19 3 0
0 0 0 211/65 3
0 0 0 2 5
r5-(130/211)r4
5 3 0 0 0
0 19/5 3 0 0
0 0 65/19 3 0
0 0 0 211/65 3
0 0 0 0 665/211
= 5*19/5*65/19*211/65*665/211
= 665.