1.2-1.4 行列式的性质(5)
发布时间：2021-06-07
2
|B|
a11 a|A|
r
s
···a1r···a···a1s···a······ a1n a|C|A|,|B|C|
0.
8(
|A|= 21
2r2s2n ···
·················· an1···anr···ans···ann ···a1s···a1r···a1n
|B|= a11 a21
···a2s···a2r···a2n ·················· ···ans
···anr
···
ann ···
an1
···a1r+a1s···a1r+a1s···a1n= a11 a21
···a2r+a2s···a2r+a2s···a2n ···
·················· an1···anr+ans···anr+ans
···
ann ···a1r···a1r+a1s···a 1n
= a11 a21···a2r···a2r+a2s···a2n
···
·················· an1···anr
···anr+ans
···ann ···a1s···a1r+a1s···a 1n
+ a11 a21···a2s···a2r+a2s···a2n
···
·················· an1
···ans···anr+ans···ann ···a 1n
=|A|+
a11···a1r···a1r a21···a2r···a2r
···a2n
···············
······ a
n1···anr···anr···ann ···a 1
n+|B|+
a11···a1s···a1s a21···a2s···a2s
···a2n
···············
······ an1···ans···ans
···ann 0,|C|
r
s
|C|=|A|+|B|=0,
|A|= |B|.r
)
|A|=a1rA1r+a2rA2r+···+anrAnr
5
2
||
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