The value of k for which the system of equations:
2x + 3y - 2z = 0; 2x - y + 3z = 0 and 7x + ky - z = 0 has non-trivial solution, is .

k = - \frac{57}{5}

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k = \frac{57}{5}

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k = - \frac{57}{10}

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k = \frac{57}{10}

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Solution

The correct option is D $k = \frac{57}{10}$
The given system of equations will have non-trivial solution if:
$D = ⎛ ⎜ ⎝ \begin{matrix} 2 & 3 & - 2 2 & - 1 & 3 7 & k & - 1 \end{matrix} ∣ ∣ ∣ ∣ = 0 \Rightarrow 2 (1 - 3 k) - 3 (- 2 - 21) - 2 (2 k + 7) = 0 \Rightarrow 2 - 6 k + 69 - 4 k - 14 = 0 \Rightarrow 10 k = 57 \Rightarrow k = \frac{57}{10}$

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