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Evaluation of a Determinant

The value of ...

Question

The value of determinant using sarrus method $∣ ∣ ∣ ∣ \begin{matrix} 1 & 2 & 3 3 & 2 & 1 2 & 1 & 0 \end{matrix} ∣ ∣ ∣ ∣$ is

A

- 10

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B

- 11

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C

0

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D

- 12

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Solution

The correct option is C $0$
Using 'Sarrus' method : $∣ ∣ ∣ ∣ \begin{matrix} a_{1} & b_{1} & c_{1} a_{2} & b_{2} & c_{2} a_{3} & b_{3} & c_{3} \end{matrix} ∣ ∣ ∣ ∣ = [a_{1} b_{2} c_{3} + b_{1} c_{2} a_{3} + c_{1} a_{2} b_{3}] - [a_{3} b_{2} c_{1} + b_{3} c_{2} a_{1} + c_{3} a_{2} b_{1}] = [0 + 4 + 9] - [0 + 1 + 12] = 0$

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