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#1 2012-11-12 07:38:38

princess snowwhite
Member
Registered: 2012-11-06
Posts: 29

a small confusion in LT

let T:R^n-->R^n be a LT where n>-2 and for k<=n,
let E={v1,v2,....,vk} and F={Tv1,Tv2,.....,Tvk}.
then
a>if E is LI then F is LI
b>if F is LI then E is LI
c>if F is LI then E is LD
d>if E is LI then F is LD


here i think the answer will be b.
let F be LI and E be LD. then c1v1+....+civi+....+ckvk= 0 where ci not equals to zero. then T( c1v1+....+civi+....+ckvk)= T(0)=0
or c1Tv1+...+ciTvi+....+ckTvk=0 where ci is non zero wich contradicts that F is LI, hence E must be LI
JUST TELL ME IF THERE IS ANYTHING WRONG IN THIS PROOF

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#2 2012-11-12 12:04:36

scientia
Member
Registered: 2009-11-13
Posts: 222

Re: a small confusion in LT

princess snowwhite wrote:

JUST TELL ME IF THERE IS ANYTHING WRONG IN THIS PROOF

Your proof looks fine to me. smile

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