Given the set $S$ below, find a linearly independent set $T$ so that $\spn{T}=\spn{S}$. \begin{equation*} S=\set{ \colvector{2\\-1\\2},\, \colvector{3\\0\\1},\, \colvector{1\\1\\-1},\, \colvector{5\\-1\\3} } \end{equation*}