This is a straight setup for the conclusion of Theorem BS. The hypotheses of this theorem tell us to pack the vectors of $W$ into the columns of a matrix and row-reduce,
\begin{align*}
\begin{bmatrix}
1 & 2 & 4 & 3 & 3 \\
2 & -3 & 1 & 1 & -1 \\
-1 & 1 & -1 & 1 & 0
\end{bmatrix}
&\rref
\begin{bmatrix}
\leading{1} & 0 & 2 & 0 & 1 \\
0 & \leading{1} & 1 & 0 & 1 \\
0 & 0 & 0 & \leading{1} & 0
\end{bmatrix}
\end{align*}
Pivot columns have indices $D=\set{1,\,2,\,4}$. Theorem BS tells us to form $T$ with columns $1,\,2$ and $4$ of $S$,
\begin{align*}
T&=
\set{
\colvector{1 \\ 2 \\ -1},\,
\colvector{2 \\ -3 \\ 1},\,
\colvector{3 \\ 1 \\ 1}
}
\end{align*}