set of vectors {v1, v2.......,vn} belongs to R^m where n

Question

set of vectors {v1, v2.......,vn} belongs to R^m where n<m. are vectors independent?

helder_edwin · Answer

not necesarily. for instance
$$ \large \{(1,2,3),(0,0,0)\} $$
is a linearly dependent set of two vectors in $\mathbb{R}^3$ and $2<3$.

anonymous · Answer

how to prove this?

anonymous · Answer

since you can prove that, for at least one case this is not true, therefore it can not be generalized.

anonymous · Answer

To prove that (1,2,3) and (0,0,0) are dependent:
Let us assume the contrary. If they are independent, then 
  k1* (1,2,3) + k2 * (0,0,0) = (0,0,0) implies k1 = k2 = 0. 
But, in this case, only k1 has to be 0. k2 can be any number and the expression still holds. Hence the proof.