Mathematics - Determinant Question with Solution | TestHub

$\because$ System of equations has more than one solution $\therefore \Delta ={\Delta }_1={\Delta }_2={\Delta }_3=0$ for infinite solution $\begin{array}{rl}{\Delta }_1& =\left|\begin{array}{ccc}a& 2& 3\\ b& -1& 5\\ c& -3& 2\end{array}\right|=a(13)+2(5c-2b)+3(-3b+c)\\ & =13a-13b+13c=0\end{array}$ i.c, $a-b+c=0$ or $b-c-a=0$