Answer
(a) A basis for the row space is given by
$$S=\{(-2,-4,4,5),(0,0,0,1)\}.$$
(b) The rank of the matrix is $2$.
Work Step by Step
Let $A$ be given by $$
A=
\left[\begin{array}{rrrr}{-2} & {-4} & {4} & {5} \\ {3} & {6} & {-6} & {-4} \\ {-2} & {-4} & {4} & {9}\end{array}\right].
$$
The reduced form of $A$ is given by
$$ \left[ \begin {array}{cccc} -2&-4&4&5\\ 0&0&0&1
\\ 0&0&0&0\end {array} \right]
$$
(a) A basis for the row space is given by
$$S=\{(-2,-4,4,5),(0,0,0,1)\}.$$
(b) The rank of the matrix is $2$.
