Mathematics - Determinant Question with Solution | TestHub

The system of linear equations is: $$\begin{array}{rl}& x+y+z=2\\ & 2x+y-z=3\\ & 3x+2y+kz=4\end{array}$$ As, system has unique solution. $$\begin{array}{rl}& \text{ So, }\left|\begin{array}{ccc}1& 1& 1\\ 2& 1& -1\\ 3& 2& k\end{array}\right|\ne 0\\ & \Rightarrow k+2-(2k+3)+1\ne 0\\ & \Rightarrow k\ne 0\end{array}$$ Hence, $k\in R-\{0\}\equiv S$