Linearly independent/(3,3,3), (0,4,5), (4,8,9)/Example

The three vectors

${\begin{pmatrix}3\\3\\3\end{pmatrix}},\,\,{\begin{pmatrix}0\\4\\5\end{pmatrix}}\,{\text{ and }}\,{\begin{pmatrix}4\\8\\9\end{pmatrix}}$

are linearly dependent. The equation

${}4{\begin{pmatrix}3\\3\\3\end{pmatrix}}+3{\begin{pmatrix}0\\4\\5\end{pmatrix}}-3{\begin{pmatrix}4\\8\\9\end{pmatrix}}={\begin{pmatrix}0\\0\\0\end{pmatrix}}\,$

is a nontrivial representation of the null vector.