1.2-1.4 行列式的性质(4)

7,|C|=|A|.

|C|

|C|=a11Q11,

Q11

n 1

2,Q11=0,n

|C|=0,∴|A|=0.

2

6|A|,|B|,|C|

′

|C|r

|A|

r

|B|r

cir=air+bir

(i=1,2,···,n).

j=r

cij=aij=bij,

|C|=|A|+|B|.1,

|C|

r=r>1,

|C|

|C|=a11Q11 a21Q21+···+( 1)n+1an1Qn1.

Qi1

Qi1=Mi1+Ni1

Qi1,Mi1,Ni1

|C|,|A|,|B|

|C|=|A|+|B|.

7

′

c6′

,

3

5

′

′

41

s

|B|,

|B|= a1s···a11···a1n a1s a11···a11···a1na2s···a21···a2n ··············· ans···an1···ann = a2s a21···a21···a2n ···············

ans an1···an1···a =

a1s a11···a1s···a1n nn a11···a1s···a1 na2s a21···a2s···a2n ··············· = a21···a2s···a2n ···············

a ns an1···ans···ann an1···ans···ann = a···a

111s···a1n a21···a2s···a2n ···············

ns···ann = |A|

an1···a

4

2

2