1.2-1.4 行列式的性质(2)

Mj1

Mj1=0,

|A|=0.

2

3

|A|

c

|B|,|B|=

c|A|.

n=1

(1)

|B|

i

|A|

i

c,

|A|

|B|=a11N11 a21N21+···+( 1)i+1cai1Ni1+···+( 1)n+1an1Nn1

Nr1

|B|

r

Nr1=cMr1,r=i,Ni1=Mi1

Mr1,Mi1(2)

|A|

|B|=c|A|.

|B|

1

|A|

1

c

|B|

|B|

i

(i>1)

|A|

i

c(

2

|A|

4

).

n

a11

a12a21)= a21

a12 ,a22 —

n=2

a21 a11

n 1

a22 =a12a21 a11a22= (a11a22 a12

n

|B|

|A|

r

r+1

Nij

|B|

i

j

|B|=a11N11 a21N21+···+( 1)r+1ar+1,1Nr1+( 1)r+2ar1Nr+1,1+···+( 1)n+1an1Nn1.

i=r,r+1,

Ni1= Mi1.|A|

i

Nr1=Mr+1,1,Nr+1,1=Mr,1,j

|B|= |A|.

j>i.

i

i+1

i+2

j

j 1

i

2(j i) 1

|B|= |A|.

2

2