Mathematics - Determinant Question with Solution | TestHub

As the system of equations has no solution then $\Delta$ should be zero and at least one of ${\Delta }_1$, ${\Delta }_2$ and ${\Delta }_3$ should not be zero. $$\begin{array}{rl}& \therefore \Delta =\left|\begin{array}{lll}1& a& 1\\ 1& 2& 2\\ 1& 5& 3\end{array}\right|=0\\ & \Rightarrow -a-1=0\Rightarrow a=-1\\ & {\Delta }_2=\left|\begin{array}{lll}1& 3& 1\\ 1& 6& 2\\ 1& b& 3\end{array}\right|\ne 0\\ & \Rightarrow b\ne 9\end{array}$$