If the trivial solution is the only solution of the system of equations $x - k y + z = 0, k x + 3 y - k z = 0, 3 x + y - z = 0$ . Then the set of all values of k is:

{2, - 3}

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R {2, - 3}

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R - {2}

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R {- 3}

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Solution

The correct option is B ${2, - 3}$
Mistake : Ans is A
As the trivial solution is then only solution then the determinant should be 0.
$∣ ∣ ∣ ∣ \begin{matrix} 1 & - k & 1 k & 3 & - k 3 & 1 & - 1 \end{matrix} ∣ ∣ ∣ ∣ = 0 ⟹ k = - 3, 2$

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