计算 Dn=|a1 a2 a3…an| |-x1 x2 0 … 0| |0 -x2 x3 …0| |… … … … … | |0 0 0 … xn |
人气:301 ℃ 时间:2020-05-18 00:10:54
解答
当xi都不等于0时
第i列提出xi,i=1,2,...,n
a1/x1 a2/x2 a3/x3 ...an/xn
-1 1 0 ...0
0 -1 1 ...0
......
0 0 0 ...1
将所有列加到第1列
按第1列展开得
Dn = x1x2...xn(a1/x1+a2/x2+...+an/xn)
= a1x2...xn+x1a2...xn+x1x2...an
讨论xi=0时上式仍成立.
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