D=
| 1 1 -1 3|
|-1 -1 2 1|
| 2 5 2 4|
| 7 2 3 2|
D=
| 1 0 0 0|
|-1 0 1 4|
| 2 3 4 -2|
| 7 -5 10 -19|
D=
|0 1 4|
|3 4 -2|
|-5 10 -19|
D=
|0 1 0|
|3 4 -18|
|-5 10 -59|
D=(-1)*
|3 -18|
|-5 -59|
D=267.老師您回答得很好，另外能否再幫忙看下這題，感激不盡
計(jì)算行列式：x+1 2 3 ...n
1 x+2 3 ...n
............ ...
1 23 ... x+n此為行和相等行列式，將第 2, 3, 4, ..., n 列均加到第1列，得
D=
|x+n(n+1)/2 2 3......... n|
|x+n(n+1)/2x+23.........n|
|x+n(n+1)/2 2 x+3.........n|
|.........................................................|
|x+n(n+1)/2 2 3.........x+n|
D=
|x+n(n+1)/2 2 3......... n|
|0x 0......... 0|
|00 x......... 0|
|........................................................|
|00 0......... x|
D=x^(n-1)*[x+n(n-1)/2]