Given system of equations are

$x+y+z=9$

$2x+5y+7z=52$

$x+7y+11z=77$

Augmented matrix$=\left[\begin{array}{llll}1& 1& 1& 9\\ 2& 5& 7& 52\\ 1& 7& 11& 77\end{array}\right]$

$R_2\to R_2-2R_1, R_3\to R_3-R_1$

$=\left[\begin{array}{cccc}1& 1& 1& 9\\ 0& 3& 5& 34\\ 0& 6& 10& 68\end{array}\right]$

$R_3\to R_3-2R_2$

$=\left[\begin{array}{llll}1& 1& 1& 9\\ 0& 3& 5& 34\\ 0& 0& 0& 0\end{array}\right]$

Here, $n\left(A\right)=n\left(AB\right)<n$.

$\therefore$The system has a infinite number of solutions