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The system of equations $- k x + 3 y - 14 z = 25; - 15 x + 4 y - k z = 3; - 4 x + y + 3 z = 4$ has unique solution then for all k in the set

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$R$

$R - {- 11, 13}$

$R - {13}$

$R - {- 11, 11}$

answer is D.

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Detailed Solution

$Δ = |\begin{matrix} - k & 3 & - 14 \\ - 15 & 4 & - k \\ - 4 & 1 & 3 \end{matrix}| = 121 - k^{2} \neq 0$

For $k \in R - {- 11, 11}$ ,the system of equations has unique solution.

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