Answer
(a) A basis for the row space is,
$$S=\left\{(1,0),(0,1)\right\}.$$
(b) The rank of the matrix is $2$.
Work Step by Step
Given the matrix
$$
\left[ \begin {array}{cc} 1&2\\ -4&3
\\ 6&1\end {array} \right]
.
$$
The reduced row echelon form is given by
$$
\left[ \begin {array}{cc} 1&0\\ 0&1
\\ 0&0\end {array} \right]
.
$$
(a) A basis for the row space is,
$$S=\left\{(1,0),(0,1)\right\}.$$
(b) The rank of the matrix is $2$.
