For the linear transformation $S$ compute the pre-images. \begin{align*} \ltdefn{S}{\complex{3}}{\complex{3}},\quad \lt{S}{\colvector{a\\b\\c}}= \colvector{a-2b-c\\3a-b+2c\\a+b+2c } \end{align*} \begin{align*} \preimage{S}{\colvector{-2\\5\\3}}& & \preimage{S}{\colvector{-5\\5\\7}}& \end{align*}