Vector spaces : linear independence need help

Prove that if the vectors v1,v2,..vn are linearly dependent vectors in Rm and if Vn+1 is any other vector in Rm, then the set v1,v2,..., vn, vn+1 is linearly dependent.

Thanks for your help.

By hypothesis, there exist constants c(1), c(2), ..., c(n) not all zero such that
c(1) v(1) + c(2) v(2) + ... + c(n) v(n) = 0.

We can rewrite this as
c(1) v(1) + c(2) v(2) + ... + c(n) v(n) + c(n+1) v(n+1) = 0, where c(n+1) = 0.

However, since c(1), c(2), ..., c(n), c(n+1) are not all 0, we conclude that
{v(1), v(2), ... , v(n), v(n+1)} is linearly dependent as well.

I hope this helps!