A) R-{2,-3}
B) R-{2}
C) R-{-3}
D) {2,-3}
Correct Answer: A
Solution :
\[x-ky+z=0\] \[kx+3y-kz=0\] \[3x+y-z=0\]this equation will have non trivial solution if \[\left| \begin{matrix} 1 & -k & 1 \\ k & 3 & -k \\ 3 & 1 & -1 \\ \end{matrix} \right|=0\] \[1(-3+k)+k(-k+3k)+1(k-9)=0\] \[k-3+2{{k}^{2}}+k-9=0\] \[2{{k}^{2}}+2k-12=0\] \[{{k}^{2}}+k-6=0\] \[k=-3,k=2\]so the equation will have only trivial solution when\[k\in R-\{2,-3\}\]
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