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