If the matrix $A=\left[\begin{array}{cccc}1& 2& 3& 0\\ 2& 4& 3& 2\\ 3& 2& 1& 3\\ 6& 8& 7& \alpha \end{array}\right]$is of rank $3$  Then $\alpha =$

$A=\left[\begin{array}{cccc}1& 2& 3& 0\\ 2& 4& 3& 2\\ 3& 2& 1& 3\\ 6& 8& 7& \alpha \end{array}\right]$

$$\begin{gathered} R_2-2R_1 \\ {R}_3-3R_1 \\ {R}_4-6R_1 \end{gathered}$$$~\left[\begin{array}{cccc}1& 2& 3& 0\\ 0& 0& -3& 2\\ 0& -4& -8& 3\\ 0& -4& -11& \alpha \end{array}\right]$

$$\begin{gathered} R_2\to R_3 \\ {R}_4-R_3 \end{gathered}$$$~\left[\begin{array}{cccc}1& 2& 3& 0\\ 0& -4& -8& 3\\ 0& 0& -3& 2\\ 0& 0& -3& \alpha -3\end{array}\right]$

$R_4-R_3$$~\left[\begin{array}{cccc}1& 2& 3& 0\\ 0& -4& -8& 3\\ 0& 0& -3& 2\\ 0& 0& 0& \alpha -5\end{array}\right]$

Rank$A=3\Rightarrow \alpha -5=0\Rightarrow \alpha =5$