1 2 3 4
2 3 4 1
3 4 1 2
4 1 2 3
按第三列展开得；
2 3 1 1 2 4 1 2 4 1 2 3
3 3 4 2 - 4 3 4 2 + 2 3 1 - 2 2 3 1
4 1 3 4 1 3 4 1 3 3 4 2
①
2 3 1 0 0 1 -1 -2
3 4 2 = -1 -2 2 = =8-4=4
4 1 3 -2 -8 3 -2 -8
②
1 2 4 1 2 4 -2 -10
3 4 2 = 0 -2 -10 = =26-70=-54
4 1 3 0 -7 -13 -7 -13
③
1 2 4 1 2 4 -1 -7
2 3 1 = 0 -1 -7 = =13-49=-36
4 1 3 0 -7 -13 -7 -13
④
1 2 3 1 2 3 -1 -5
2 3 1 = 0 -1 -5 = =7-10=3
3 4 2 0 -2 -7 -2 -7
所以行列式=3×4-4×(-54)-36-2×3=186