[理工] [線代]-台大95-資工

看板Grad-ProbAsk作者 (何去何從?)時間16年前 (2010/01/06 00:32), 編輯推噓3(307)
留言10則, 3人參與, 最新討論串1/1
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.....? -- 我絕對不會說 這是我的無名......... http://www.wretch.cc/blog/chris750630 -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 203.73.27.242

01/06 00:39, , 1F
(B)(D)吧= =?
01/06 00:39, 1F

01/06 00:39, , 2F
(C)要在det(A)和det(B)都存在的情況下
01/06 00:39, 2F

01/06 00:40, , 3F
(E)det(cA) = c^n*det(A)
01/06 00:40, 3F

01/06 00:42, , 4F
(C)但若det(A)=0 -> A不可逆-> AB不可逆 ->det(AB)=0
01/06 00:42, 4F

01/06 00:42, , 5F
這有問題嘛.....?
01/06 00:42, 5F

01/06 00:43, , 6F
(A)用a11=1 a12=a13=a14=0 這個矩陣應該就沒有反矩陣了
01/06 00:43, 6F

01/06 00:44, , 7F
講錯應該是a12=a21=a22=0
01/06 00:44, 7F
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)

01/06 11:30, , 8F
(C)det(A)=0 or det(B)=0 時det(AB)=0在任何情況下都對
01/06 11:30, 8F

01/06 11:31, , 9F
所以(C)不需條件也對吧
01/06 11:31, 9F

01/06 12:09, , 10F
我瞭了
01/06 12:09, 10F
文章代碼(AID): #1BGscc1w (Grad-ProbAsk)