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Determinant

If the system...

Question

If the system of equations of $3 x - 2 y + z = 0, k x - 14 y + 15 z = 0, x + 2 y + 3 z = 0$ has non trivial solution then $k =$

A

29

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B

26

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C

23

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D

19

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Solution

The correct option is A $29$
According to the given information

$\Rightarrow ∣ ∣ ∣ ∣ \begin{matrix} 3 & - 2 & 1 k & - 14 & 15 1 & 2 & 3 \end{matrix} ∣ ∣ ∣ ∣ = 0$

$\Rightarrow 3 (- 42 - 30) + 2 (3 k - 15) + 1 (2 k + 14) = 0$

$\Rightarrow - 216 + 6 k - 30 + 2 k + 14 = 0$

$\Rightarrow 8 k = 232$

$\Rightarrow k = 29$

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