1.2-1.4 行列式的性质
发布时间：2021-06-07
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
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