推 qa77330:是用det嗎 11/26 23:02
→ iyenn:yes 11/26 23:16
→ iyenn:用det(AB)=det(A)det(B)證就輕鬆了 11/26 23:25
→ ruby791104:3題都是嗎？可不可以做一題給我參考＠＠ 11/26 23:32
嗯……
我承認這是作業，
可是我真的不會寫，
拜託好心的大大幫忙！
以下三題，討論並證明”only if”的情形。
1.Suppose A, B are in R^n＊n and A is nonsingular.
Prove that AB is singular if B is singular.
2.Suppose A, B are in R^n＊n and A-B is nonsingular.
Prove that┌ ┐ is nonsingular.
｜I I ｜
｜ ｜
｜A B ｜
└ ┘
3.Suppose A, E, F are in R^n＊n and that E and F are elementary matrices.
Prove that if A is nonsingular then EAF is nonsingular.
先在此謝過好心的大大囉！（鞠躬
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◆ From: 120.127.32.231
※ 編輯: ruby791104 來自: 120.127.32.231 (11/26 23:00)
※ 編輯: ruby791104 來自: 120.127.32.231 (11/26 23:00)
※ 編輯: ruby791104 來自: 120.127.32.231 (11/26 23:02)