2 1 -5 8
1 -3 0 9
0 2 -1 -5
1 4 -7 0
r1-2r2,r4-r2
0 7 -5 -10
1 -3 0 9
0 2 -1 -5
0 7 -7 -9
r4-r1,r1-3r3
0 1 -2 5
1 -3 0 9
0 2 -1 -5
0 0 -2 1
r3-2r1
0 1 -2 5
1 -3 0 9
0 0 3 -15
0 0 -2 1
r4+(2/3)r3
0 1 -2 5
1 -3 0 9
0 0 3 -15
0 0 0 -9
交换1,2行后为上三角
行列式 = 27.