Re: [線代] linearly dependent
※ 引述《gmnxix (果凍)》之銘言：
: 覺得好像不會很難,但突然證不出來@@
: Let the set {v1,v2} be linearly dependent in a vector space V
: Prove that {v1+v2,v1-v2}is also linearly dependent
: 初步想法:
: V2=CV1 或 C1V1+C2V2=0 C1.C2 not both0
: =>卡住ing.......QQ
There exist a and b such that
av1+bv2=0 where at least one of a and b is not zero.
Let A=a+b, B=a-b, then at least one of A and B is not zero,
and A(v1+v2)+B(v1-v2)=(a+b)(v1+v2)+(a-b)(v1-v2)
=2(av1+bv2)=2*0=0.
So v1+v2 and v1-v2 are linearly dependent.
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 123.192.216.62
討論串 (同標題文章)
本文引述了以下文章的的內容：
完整討論串 (本文為第 2 之 2 篇)：