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Cramer's Rule

x + ky - z = ...

Question

$x + k y - z = 0, 3 x - k y - z = 0$ and $x - 3 y + z = 0$ has non-zero solution for k =

A

-1

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B

1

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C

2

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Solution

The correct option is B 1
It has a non-zero solution if
$∣ ∣ ∣ ∣ \begin{matrix} 1 & k & - 1 3 & - k & - 1 1 & - 3 & 1 \end{matrix} ∣ ∣ ∣ ∣ = 0 \Rightarrow - 6 k + 6 = 0 \Rightarrow k = 1 .$

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