Question

线性代数行列式问题,要求用行列式性质解,

Answer 1

3-2r1-2r2,r1-4r2

0 -7 2 -4

1 2 0 2

0 -1 -2 -12

0 1 1 7

r1r2

1 2 0 2

0 -7 2 -4

0 -1 -2 -12

0 1 1 7

r2-7r3,r4+r3

1 2 0 2

0 0 16 80

0 -1 -2 -12

0 0 -1 -5

-- 2,4行成比例,故

行列式 = 0