求下列两个行列式的值答案分别为6和x^n+(-1)^(n+1)*y^n

2 1 0 0 0
1 2 1 0 0
0 1 2 1 0
0 0 1 2 1
0 0 0 1 2
r2-(1/2)r1
2 1 0 0 0
0 3/2 1 0 0
0 1 2 1 0
0 0 1 2 1
0 0 0 1 2
r3-(2/3)r2
2 1 0 0 0
0 3/2 1 0 0
0 0 4/3 1 0
0 0 1 2 1
0 0 0 1 2
r4-(3/4)r3
2 1 0 0 0
0 3/2 1 0 0
0 0 4/3 1 0
0 0 0 5/4 1
0 0 0 1 2
r5-(4/5)r4
2 1 0 0 0
0 3/2 1 0 0
0 0 4/3 1 0
0 0 0 5/4 1
0 0 0 0 6/5
= 2*3/2*4/3*5/4*6/5
= 6
第二题直接用行列式的展开定义可得
D = x^n + (-1)^t(234...n1) y^n
= x^n + (-1)^(n-1) y^n