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 :
Solutions · 1
Official solution
As system of linear equations have unique solutions so, determinant of coefficient \[ \ne \] 0
\[ \therefore \] \[\left| {1231121−1k } \right|\] \[ \ne \] 0
\[ \Rightarrow \] k + 2 - (2k + 3) + 1 \[ \ne \] 0
\[ \Rightarrow \] k \[ \ne \] 0
\[ \therefore \] k \[ \in \] R - {0}