Question

行列式D=(1 -5 3 -3)(2 0 1 -1)(-513-4)(-513-4)(31-12)

Answer 1

行列式 =

1 -5 3 -3

2 0 1 -1

-5 1 3 -4

3 1 -1 2

r2-2r1,r3+5r1,r4-3r1

1 -5 3 -3

0 10 -5 5

0 -24 18 -19

0 16 -10 11

第2行提出5,D=5*

1 -5 3 -3

0 2 -1 1

0 -24 18 -19

0 16 -10 11

r3+12r2,r4-8r2

1 -5 3 -3

0 2 -1 1

0 0 6 -7

0 0 -2 3

r3+3r4

1 -5 3 -3

0 2 -1 1

0 0 0 2

0 0 -2 3

r4*(-1),r3r4

1 -5 3 -3

0 2 -1 1

0 0 2 -3

0 0 0 2

D = 5*2*2*2 = 40.