= Solution
The <pivot columns> of the reduced matrix in part (i) are columns one and two. Select those columns of the original matrix, giving the <column-space basis>
$$
\boxed{\left\{\begin{pmatrix}-3\\-1\\2\end{pmatrix},\begin{pmatrix}4\\2\\1\end{pmatrix}\right\}.}
$$
They are independent, for example their first two entries have determinant $-2\ne0$. The remaining original column is the first plus twice the second. Taking the reduced matrix's columns instead would generally give the wrong <column space>.
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