1.2-1.4 行列式的性质

IP

59.77.1.116;

§1.2-§1.4

(

10);

Cramer1

|A|=a11a22···ann(

|A| a11 0|A|= ···

0

n

a12a22···0

············aii

a1n a2n ··· ann

|A|

a11 a21

|A|= ···

an1

0a22···an2············

).

0 0 ··· ann

(1)|A|

n=1

|A|=a11

n 1

n

|A|.

|A|=a11M11.

M11

n 1

M11=a22a33···ann,

|A|=a11a22···ann.

(2)|A|

|A|=a11M11 a21M21+···+( 1)n+1an1Mn1.

n 1

Mi1,i>1,

Mi1

Mi1=0,i>1,|A|

M11

M11=a22···ann.|A|

|A|=a11a22···ann.

2

2

n=1

n 1

|A|

i

|A|=a11M11 a21M21+···+( 1)n+1an1Mn1

Mj1(j=i)

Mj1=0,

ai1=0,

ai1Mi1=0,

|A|=0.i

|A|

i=1,

|A|=0.

i>1,

|A|=a11M11 a21M21+···+( 1)n+1an1Mn1

1