Answer
(a) A basis for the row space is given by
$$S=\{(1,-3,2),(0,14,7)\}.$$
(b) The rank of the matrix is $2$.
Work Step by Step
Let $A$ be given by $$
A=\left[\begin{array}{rrr}{1} & {-3} & {2} \\ {4} & {2} & {1}\end{array}\right]
$$
The reduced form of $A$ is given by
$$\left[ \begin {array}{ccc} 1&-3&2\\ 0&14&-7
\end {array} \right]
$$
(a) A basis for the row space is given by
$$S=\{(1,-3,2),(0,14,7)\}.$$
(b) The rank of the matrix is $2$.
