Kernel and image of a matrix mapping

Let \(L_A: \mathbb{R}^3\longrightarrow \mathbb{R}^3\) be the linear mapping determined by the matrix \[A=\matrix{0 & -4 & 4 \\ 0 & 2 & -2 \\ 0 & -1 & 1 \\ }\tiny. \] Calculate a vector \(\vec{v}\) that spans the image of \(L_A\).

\(\vec{v}={}\)

#\cv{\Box \\ \Box \\ \Box}#