Answer
(a) A basis for the row space is,
$$S=\left\{(1,0,\frac{26}{11}),(0,1,\frac {8}{11})\right\}.$$
(b) The rank of the matrix is $2$.
Work Step by Step
Given the matrix
$$
\left[ \begin {array}{ccc} 2&-1&4\\ 1&5&6
\\ 1&16&14\end {array} \right]
.
$$
The reduced row echelon form is given by
$$
\left[ \begin {array}{ccc} 1&0&\frac{26}{11}\\ 0
&1&{\frac {8}{11}}\\ 0&0&0\end {array} \right]
.
$$
(a) A basis for the row space is,
$$S=\left\{(1,0,\frac{26}{11}),(0,1,\frac {8}{11})\right\}.$$
(b) The rank of the matrix is $2$.
