1.2-1.4 行列式的性质(8)
发布时间：2021-06-07
n
a11x1+a12x2+···+a1nxn=b1
a21x1+a22x2+···+a2nxn=b2
···
an1x1+an2x2+···+annxn=bn
(2)
|A|
ξ1,ξ2,···,ξn,
a11 a21
|A|= ···
an1
a12a22···an2
············
1
a1n a2n ··· ann
A11,A21,···,An1,
A11
(1)
1
A21(1)2···,An1(1)n
a11A11ξ1+a12A11ξ2+···+a1nA11ξn=b1A11
a21A21ξ1+a22A21ξ2+···+a2nA21ξn=b2A21
···
an1An1ξ1+an2An1ξ2+···+annAn1ξn=bnAn1
(3)
(a11A11+a21A21+···+an1An1)ξ1+(a12A11+a22A21+···+
b1a12
b2a22
|A|ξ1= ······
bnan2
an2An1)ξ2+···+(a1nA11+a2nA21+···+annAn1)ξn=b1A11+b2A21+···+bnAn1.
10
············j
A1.
|A|=0,
ξ1=
A1
a1n a2n ,··· ann
|A|
,2≤j≤n,
Aj
n
|A|
b1,b2,···,bn
(Cramer
)n
a11x1+a12x2+···+a1nxn=b1
a21x1+a22x2+···+a2nxn=b2
···
an1x1+an2x2+···+annxn=bn
8
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