# Finding a certain vector $w \in \mathbb{R}^{3}$.

Let $A = \begin{pmatrix} 1 & 4 & -2 & 2 \\ 0 & 1 & 2 & -5 \\ 2 & 6 & -8 & 14 \end{pmatrix}$.

Find a vector $w \in \mathbb{R}^{3}$ that is not in the image of the linear transformation $x \longmapsto Ax$.

Note: $A$ is a $(3 \times 4)$-matrix.