※ 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 For n when n=2 ┌ a b ┐ A=│ │ then det(A)=ab-ba=0 └ a b ┘ set for k=n is OK now that k=n+1,A:(n+1)×(n+1) and for A, r row and s row is same because n>=3 choose i!=r & i!=s n+1 i+j det(A)=Σ (-1) aij*det(Aij) j=1 det(Aij):n×n det(Aij)=0 so for k=n is OK k=n+1 is OK @@ 其实我是想打中文的XDD 不过看到题目用英文问 就直接打英文了 然後 aij 的 ij 是下标 不过我不会用bbs打下标 同理 Aij 的ij也是下标 然後i+j是(-1)的次方 : 2.Let A and B be 2 ×2 matrices. : (a)Does det(A+B) = det(A) + det(B)？ : (b)Does det(AB) = det(A)det(B)？ : (c)Does det(AB) = det(BA)？ : Justify answers. : 3.Let A and B be 2 ×2 matrices and let : ┌ ┐ ┌ ┐ ┌ ┐ : │a11 a12│ │b11 b12│ │0 α│ : C = │ │ D = │ │ E = │ │ : │b21 b22│ │a21 a22│ │β 0│ : └ ┘ └ ┘ └ ┘ : (a)Show that det(A+B) = det(A) + det(B) + det(C) + det(D) : (b)Show that if B = EA then det(A+B) = det(A) + det(B) : 以上，麻烦好心的大大！（鞠躬 --

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