Linear dependence of three vectors

Question

Could someone please explain why, if two vectors in a set of three are parallel to each other, that this implies that the whole set of three vectors is linearly dependent? I have tried to show this algebraically and to understand it graphically but I simply cannot see how one implies the other.

Answer 1

The vectors would be, say, $\mathbf v$, $k\mathbf v$ and $\mathbf w$. Then $$k\mathbf{v}+(-1)k\mathbf{v}+0\cdot\mathbf{w}=\mathbf{0}$$