c1+c2+c3+c4+c5
15 2 3 4 5
15 3 4 5 1
15 4 5 1 2
15 5 1 2 3
15 1 2 3 4

r5-r4,r4-r3,r3-r2.r2-r1
15 2 3 4 5
0 1 1 1 -4
0 1 1 -4 1
0 1 -4 1 1
0 -4 1 1 1

按第1列展开
= (-1)^(1+1)* 15 *
1 1 1 -4
1 1 -4 1
1 -4 1 1
-4 1 1 1

c1+c2+c3+c4
-1 1 1 -4
-1 1 -4 1
-1 -4 1 1
-1 1 1 1

c2+c1,c3+c1,c4+c1
-1 0 0 -5
-1 0 -5 0
-1 -5 0 0
-1 0 0 0

= 15*(-1)*(-5)^3
= 1875.