Answer
(a) A basis for the column space are the columns corresponding to the columns that have the leading 1's. That is,
$$S=\left\{\left[\begin{array}{ll}{2} \\ {1} \end{array}\right],\left[\begin{array}{ll} {4} \\ {6}\end{array}\right]\right\}.$$
(b) The rank of the matrix is $2$.
Work Step by Step
Given the matrix
$$
\left[\begin{array}{ll}{2} & {4} \\ {1} & {6}\end{array}\right].
$$
The reduced row echelon form is given by
$$
\left[ \begin {array}{cc} 1&0\\0&1\end {array}
\right].$$
(a) A basis for the column space are the columns corresponding to the columns that have the leading 1's. That is,
$$S=\left\{\left[\begin{array}{ll}{2} \\ {1} \end{array}\right],\left[\begin{array}{ll} {4} \\ {6}\end{array}\right]\right\}.$$
(b) The rank of the matrix is $2$.