A value of  $b$ for which the rank of the matrix  is $A=\left[\begin{array}{cccc}1& 1& -1& 0\\ 4& 4& -3& 1\\ b& 2& 2& 2\\ 9& 9& b& 3\end{array}\right]$is 3, is

$\left[\begin{array}{cccc}1& 1& -1& 0\\ 4& 4& -3& 1\\ b& 2& 2& 2\\ 9& 9& b& 3\end{array}\right]$$\begin{array}{l}{R}_2\to R_2-4R_1\\ R_3\to R_3-b{R}_1\\ R_4\to R_4-9R_1\end{array}$

$~\left[\begin{array}{cccc}1& 1& -1& 0\\ 0& 0& 1& 1\\ 0& 2-b& 2+b& 2\\ 0& 0& b+9& 3\end{array}\right]$$R_2\leftrightarrow R_3$

$~\left[\begin{array}{cccc}1& 1& -1& 0\\ 0& 2-b& 2+b& 2\\ 0& 0& 1& 1\\ 0& 0& b+9& 3\end{array}\right]$$R_4\to R_4-3R_3$

$~\left[\begin{array}{cccc}1& 1& -1& 0\\ 0& 2-b& 2+b& 2\\ 0& 0& 1& 1\\ 0& 0& b+6& 0\end{array}\right]$

Rank of$A=3\Rightarrow b+6=0$

                             $\Rightarrow b=-6$