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Evaluation of a Determinant

The value of ...

Question

The value of the determinant $∣ ∣ ∣ ∣ \begin{matrix} 4 & - 6 & 1 - 1 & - 1 & 1 - 4 & 11 & - 1 \end{matrix} ∣ ∣ ∣ ∣$ is

A

-75

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B

25

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C

\N

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D

-25

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Solution

The correct option is D -25
$∣ ∣ ∣ ∣ \begin{matrix} 4 & - 6 & 1 - 1 & - 1 & 1 - 4 & 11 & - 1 \end{matrix} ∣ ∣ ∣ ∣ = ∣ ∣ ∣ ∣ \begin{matrix} 0 & 5 & 0 - 1 & - 1 & 1 - 4 & 11 & - 1 \end{matrix} ∣ ∣ ∣ ∣ {A p p l i n g R_{1} \to R_{1} + R_{3}} = - 5 (1 + 4) = - 25$ .

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