Discussion @ 1041. Nikifor @ Timus Online Judge

There is still no answer to the question - What is "linearly independent vectors" ? ? ?

Posted by Georgi Tsankov 19 Oct 2001 12:27

subj.

Re: There is still no answer to the question - What is "linearly independent vectors" ? ? ?

Posted by Marat Bakirov 20 Oct 2001 13:51

Vectors x1,... xn are linery dependent iff
there exist numbers a1,...an such that a1^2 + ... + an^2 !
= 0
and a1*x1+a2*x2 .... + an*xn = 0

Vectors are independent otherwise.

Re: There is still no answer to the question - What is "linearly independent vectors" ? ? ?

Posted by awts 20 Apr 2003 18:32

as your explanation 0 0 3 is a linery independed vector,isn't it?

Re: There is still no answer to the question - What is "linearly independent vectors" ? ? ?

Posted by 198808xc 15 Feb 2005 20:00

Can I consider it like this:
Vectors x1,... xn are linery dependent iff

for any two vectors (xi,xj) in {x1,x2...xn}, there doesn't exist a real number K that
x[i,l]*K=x[j,l] (l=1,2...n).

Please help me.
Thanks very much!

Counter example

Posted by Vlad Veselov [PMG17,Vinnitsa - KNU,Kiev] 17 Feb 2005 17:39

x1=(1;0;0)
x2=(0;1;1)
x3=(1;1;1)

My opinion (I don't know correct or not)

Posted by Maigo Akisame (maigoakisame@yahoo.com.cn) 19 Dec 2005 12:34

Vectors v1,v2,...,vn are linearly independent iff for any vi, you CAN'T find a set of real numbers (a1,a2,...,a(i-1),a(i+1),...,an) such that vi=a1*v1+a2*v2+...+a(i-1)*v(i-1)+a(i+1)*v(i+1)+...+an*vn.
That means for any n-dimensional vector v, you CAN find a set of real numbers (a1,a2...an) such that v=a1*v1+a2*v2+...+an*vn.

Discussion of Problem 1041. Nikifor