Consider the system of linear equations:

$x_1+2x_2+x_3=3$

$2x_1+3x_2+x_3=3$

$3x_1+5x_2+2x_3=1$

The system has

no solution

The correct answer is option (2) : no solution

We have,

$D=\begin{vmatrix}1 & 2 & 1\\2 & 3 & 1\\3 & 5 & 2\end{vmatrix}=0, $ and $D_1= \begin{vmatrix}3 & 2 & 1\\3 & 3 & 1\\1 & 5 & 2\end{vmatrix}≠0$

So, the given system of equations has no solution.