Mathematics - Determinant Question with Solution | TestHub

$\begin{array}{rl}& 2x-y+z=4\\ & 5x+\lambda y+3z=12\\ & 100x-47y+\mu z=212\\ & \Delta x=\Delta y=\Delta z=0\\ & \Delta z=\left|\begin{array}{ccc}2& -1& 4\\ 5& \lambda & 12\\ 100& -47& 212\end{array}\right|=0\\ & \Rightarrow 2(212\lambda +564)+1(1060-1200)\\ & \Rightarrow 424\lambda +1128-140-940-400\lambda =0\\ & \Rightarrow \lambda =-2\\ & \Delta y=\left|\begin{array}{ccc}2& -1& 1\\ 5& -2& 3\\ 100& -47& \mu \end{array}\right|=0\\ & \Rightarrow 2(-2\mu +141)+1(5\mu -300)+1(-235+200)=0\\ & \Rightarrow \mu =53\\ & \mu -2\lambda =53-2(-2)=57\end{array}$