JUST TELL ME IF THERE IS ANYTHING WRONG IN THIS PROOF

Your proof looks fine to me.

]]>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