[理工] [線代]-台大95-資工

[chris750630 (何去何從？)]

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) -> ... 這三小？

(E) det(cA) = c^(n-1)*det(A)  -> ...... Q__Q

所以正確的到底是.....?

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我絕對不會說 這是我的無名.........

http://www.wretch.cc/blog/chris750630

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◆ From: 203.73.27.242
推 shinyhaung:(B)(D)吧=  =?
→ shinyhaung:(C)要在det(A)和det(B)都存在的情況下
→ shinyhaung:(E)det(cA) = c^n*det(A)
→ chris750630:(C)但若det(A)=0 -> A不可逆-> AB不可逆 ->det(AB)=0
→ chris750630:這有問題嘛.....？
推 shinyhaung:(A)用a11=1 a12=a13=a14=0 這個矩陣應該就沒有反矩陣了
→ shinyhaung:講錯應該是a12=a21=a22=0
剛猛然看到第(A)項少打了不等於零... 已補上
※ 編輯: chris750630     來自: 203.73.27.242        (01/06 00:46)
推 shine17:(C)det(A)=0 or det(B)=0 時det(AB)=0在任何情況下都對
→ shine17:所以(C)不需條件也對吧
→ chris750630:我瞭了