Answer
(a) A basis for the column space is
$$S=\{\left[1\right]\}.$$
(b) The rank of the matrix is $1$.
Work Step by Step
Given the matrix
$$
\left[\begin{array}{lll}{1} & {2} & {3}\end{array}\right]
$$
The reduced row echelon form is given by
$$
\left[\begin{array}{lll}{1} & {2} & {3}\end{array}\right]
$$
(a) A basis for the column space are the columns corresponding to the columns that have the leading 1's. That is,
$$S=\{\left[1\right]\}.$$
(b) The rank of the matrix is $1$.