Re: [線代] 兩題證明
※ 引述《tim8238818 (AAAAAAAAAAAAAAAAAAAAAAA)》之銘言：
: Prove that if A is an n x n skew symmetric matrix where n is odd,
: then det(A) = 0.
: Let A be an n x n invertible matrix. Prove that at least one of the matrices
: associated with the minors, Mij, must be invertible
: 第一題我應該會用數學歸納法做
: 但是det(A)=0我一直想不到怎麼寫
: 第二題就沒什麼頭緒
: 有點想用反證法，但是不知道怎麼開頭
: 先謝謝板上神人的不吝指教
1.A^T=-A
detA
=det(A^T)
=det(-A)
=(-1)^n*(detA)...det(kA)=(k^n)(detA),出現在Steven J.Leon的線代習題.
=-detA
如此一來,2detA=0,detA=0.
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※ 編輯: wayne2011 (61.58.103.35), 03/28/2016 10:14:23
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