Answer
(a) A basis for the row space is,
$$S=\left\{(1,2,-1)\right\}.$$
(b) The rank of the matrix is $1$.
Work Step by Step
Given the matrix
$$
\left[ \begin {array}{ccc} 1&2&-1\end {array} \right]
.
$$
The reduced row echelon form is given by
$$
\left[ \begin {array}{ccc} 1&2&-1\end {array} \right]
.
$$
(a) A basis for the row space is,
$$S=\left\{(1,2,-1)\right\}.$$
(b) The rank of the matrix is $1$.
