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 \[A=\matrix{-3 & -3 & 1 \\ 3 & 3 & -1 \\ -9 & -9 & 3 \\ }\tiny. \] Calculate a vector \(\vec{v}\) that spans the image of \(L_A\).

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

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