Question

求矩阵A=det（a1,a2,a3,a4)的行列式,a1=(1,1,1,1),a2=(1,1,-1,-1),a3=(1,

Answer 1

|A|=

1 1 1 1

1 1 -1 1

1 -1 1 -1

1 -1 -1 1

r4-r3,r2-r1,r3-r1

1 1 1 1

0 0 -2 0

0 -2 0 -2

0 0 -2 2

r4-r2

1 1 1 1

0 0 -2 0

0 -2 0 -2

0 0 0 2

r2r3 (行列式变符号)

1 1 1 1

0 -2 0 -2

0 0 -2 0

0 0 0 2

= -8.