求解11233-1-1-223-1-1123-1四介行列式答案有要解答过程

Question

求解1123 3-1-1-2 23-1-1 123-1四介行列式
答案有 要解答过程

Answer 1

|1 1 2 3|
3 -1 -1 -2
2 3 -1 -1
1 2 3 -1

=|1 1 2 3|
0 -4 -7 -11 【r2-r1*3
0 1 -5 -7 r3-r1*2
0 1 1 -4 r4-r1

=|1 1 2 3|
0 0 -3 -27 【r2+r4*4
0 0 -6 -3 r3-r4
0 1 1 -4

=|1 1 2 3|
0 0 -3 -27
0 0 0 51 【r3-r2*2
0 1 1 -4

=|1 1 2 3|
0 1 1 -4 【r4与r3交换、r3与r2交换，两次交换行列式符号不变
0 0 -3 -27
0 0 0 51
=-153