Let S be the set of all real values of k for which the systemof linear equations
x + y + z = 2
2x + y − z = 3
3x + 2y + kz = 4
has a unique solution. Then S is :

equal to R - {0}

As system of linear equations have unique solutions so, determinant of coefficient ≠ 0

\( ∴ \begin{vmatrix}1 & 1 & 1\\2 & 1 & -1\\ 3& 2 & k\end{vmatrix}≠ 0\)

\(⇒ k + 2 - ( 2k + 3) + 1 ≠ 0\)

\(⇒ k ≠ 0\)

\( ∴ k \in - \) {0}