求行列式,I1 2 2 2...2II2 2 2 2...2II2 2 3 2...2II.II2 2 2 2...nI

求行列式,I1 2 2 2...2II2 2 2 2...2II2 2 3 2...2II.II2 2 2 2...nI
求行列式,
I1 2 2 2...2I
I2 2 2 2...2I
I2 2 3 2...2I
I.I
I2 2 2 2...nI

求行列式,I1 2 2 2...2II2 2 2 2...2II2 2 3 2...2II.II2 2 2 2...nI
1 2 2 2...2
2 2 2 2...2
2 2 3 2...2
.
2 2 2 2...n --> 所有行减去第二行
-10 0 0...0 0
2 2 2 2...2 2
0 0 1 0...0 0
.
0 0 0 0...n-3 0
0 0 0 0...0 n-2 --> 按第一行展开
2 2 2...2 2
0 1 0...0 0
.* 1 *（-1)
0 0 0 0...n-3 0
0 0 0 0...0 n-2
= 1 *（-1)^(2+1）*｛2*(n-2)!｝
= -2*(n-2)!