作者ruby791104 (阿年：）)
看板Grad-ProbAsk
标题[理工] [线代]-三题证明题，请大大们帮忙！
时间Thu Nov 26 22:57:43 2009
嗯……
我承认这是作业，
可是我真的不会写，
拜托好心的大大帮忙！
以下三题，讨论并证明”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.
先在此谢过好心的大大罗！（鞠躬
--
※ 发信站: 批踢踢实业坊(ptt.cc)
◆ From: 120.127.32.231
※ 编辑: ruby791104 来自: 120.127.32.231 (11/26 23:00)
※ 编辑: ruby791104 来自: 120.127.32.231 (11/26 23:00)
※ 编辑: ruby791104 来自: 120.127.32.231 (11/26 23:02)
1F：推 qa77330:是用det吗 11/26 23:02
2F：→ iyenn:yes 11/26 23:16
3F：→ iyenn:用det(AB)=det(A)det(B)证就轻松了 11/26 23:25
4F：→ ruby791104:3题都是吗？可不可以做一题给我参考＠＠ 11/26 23:32