In Example RAO the range of Archetype O was determined to be \begin{equation*} \rng{T}=\spn{\set{ \colvector{1\\0\\-3\\-7\\-2},\,\colvector{0\\1\\2\\5\\1} } }\end{equation*} a subspace of dimension 2 in $\complex{5}$. Since $\rng{T}\neq\complex{5}$, Theorem RSLT says $T$ is not surjective.