The equations
$3 x - y + z = 0$
$- 15 x + 6 y - 5 z = 0$
$5 x - 2 y + 2 z = 0$
have .................... solution.

trivial

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inconsistent

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infinite

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no solution

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Solution

The correct option is A trivial
$∣ ∣ ∣ ∣ \begin{matrix} 3 & - 1 & 1 - 15 & 6 & - 5 5 & - 2 & 2 \end{matrix} ∣ ∣ ∣ ∣ = 3 (2) + (- 30 + 25) = 1$
$Δ \neq 0$
$∴$ Given system has trivial solution.
Hence, option A.

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