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If trivial solution is the only solution of the system of linear equations xky+z=0,kx+3ykz=0,3x+yz=0 then set of all values of ‘k’ is

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a
R−{2,−3}
b
R−{2}
c
R−{3}
d
R−{-2,−3}

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detailed solution

Correct option is A

The system of equations will have only trivial solution if 1−k1k3−k31−1≠0⇒1(-3+k)+k(-k+3k)+1(k-9)≠0⇒k2+k-6≠0⇒k≠2,-3∴k∈R-{2,-3}


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