A) An empty set
B) Equal to \[R-\{0\}\]
C) Equal to \[\{0\}\]
D) Equal to \[R\]
Correct Answer: B
Solution :
Given are the system of linear equations. \[x+y+z=2\] \[2x+y-z=3\] \[3x+2y+kz=4\] We know that, this system has a unique solution. Therefore, coefficient determinant is non-zero. \[\left| \begin{matrix} 1 & 1 & 1 \\ 2 & 1 & -1 \\ 3 & 2 & k \\ \end{matrix} \right|\ne 0\] \[\Rightarrow k+2-(2k+3)+1\ne 0\] \[\Rightarrow k\ne 0\] Therefore, \[k\in R-\{0\}\equiv S\]
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