作者yyc2008 ()
看板Grad-ProbAsk
标题Re: [理工] [线代]-行列式证明题
时间Thu Dec 3 17:26:34 2009
※ 引述《ruby791104 (阿年:))》之铭言:
: 1.Use mathematical induction to prove that if A is an (n+1) ×(n+1) matrix
: with two identical rows then det(A) = 0
Case n=0 is trivial.
If it is true for n×n matrix,
then for (n+1) ×(n+1) matrix,
we can use raw expansion with respect to some raw not any one of two
identical rows given.
By the assumption, every term is 0.
QED.
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