作者chris750630 (何去何从？)
看板Grad-ProbAsk
标题[理工] [线代]-台大95-资工
时间Wed Jan 6 00:32:36 2010
3.
Let det(A) be the determinant of matrix A (- R^(n*n)
Which are correct?
(A) det(A) != 0 <=> A invertible. -> wrong
(B) det(A^T) = det(A) -> not sure , but right , I guess.
(C) det(AB) = det(A)*det(B) -> not sure , but right , I guess.
(D) A is invertible => det(A^(-1)) = det(A)^(-1) -> ... 这三小？
(E) det(cA) = c^(n-1)*det(A) -> ...... Q__Q
所以正确的到底是.....?
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http://www.wretch.cc/blog/chris750630
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※ 发信站: 批踢踢实业坊(ptt.cc)
◆ From: 203.73.27.242
1F：推 shinyhaung:(B)(D)吧= =? 01/06 00:39
2F：→ shinyhaung:(C)要在det(A)和det(B)都存在的情况下 01/06 00:39
3F：→ shinyhaung:(E)det(cA) = c^n*det(A) 01/06 00:40
4F：→ chris750630:(C)但若det(A)=0 -> A不可逆-> AB不可逆 ->det(AB)=0 01/06 00:42
5F：→ chris750630:这有问题嘛.....？ 01/06 00:42
6F：推 shinyhaung:(A)用a11=1 a12=a13=a14=0 这个矩阵应该就没有反矩阵了 01/06 00:43
7F：→ shinyhaung:讲错应该是a12=a21=a22=0 01/06 00:44
刚猛然看到第(A)项少打了不等於零... 已补上
※ 编辑: chris750630 来自: 203.73.27.242 (01/06 00:46)
8F：推 shine17:(C)det(A)=0 or det(B)=0 时det(AB)=0在任何情况下都对 01/06 11:30
9F：→ shine17:所以(C)不需条件也对吧 01/06 11:31
10F：→ chris750630:我了了 01/06 12:09