1 amp; 1 amp; 1 1 amp; 1+x amp; 1 1 amp; 1 amp; 1+y = 0 amp; 0 amp; 1 x amp; x amp; 1 0 amp; y amp; 1+y =xy, [ C_1 → C ...

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Properties of Determinants

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Question

$∣ ∣ ∣ ∣ \begin{matrix} 1 & 1 & 1 1 & 1 + x & 1 1 & 1 & 1 + y \end{matrix} ∣ ∣ ∣ ∣ =$

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Solution

The correct option is D xy
$∣ ∣ ∣ ∣ \begin{matrix} 1 & 1 & 1 1 & 1 + x & 1 1 & 1 & 1 + y \end{matrix} ∣ ∣ ∣ ∣ = ∣ ∣ ∣ ∣ \begin{matrix} 0 & 0 & 1 - x & x & 1 0 & - y & 1 + y \end{matrix} ∣ ∣ ∣ ∣ = x y, (\begin{matrix} C_{1} \to C_{1} - C_{2} C_{2} \to C_{2} - C_{3} \end{matrix}) .$

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