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 \[A=\matrix{15 & 6 & -6 \\ -25 & -10 & 10 \\ 5 & 2 & -2 \\ }\tiny. \] Calculate a vector \(\vec{v}\) that spans the image of \(L_A\).

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

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