$∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 & b c & a (b + c) 1 & c a & b (c + a) 1 & a b & c (a + b) \end{matrix} ∣ ∣ ∣ ∣ ∣ =$

0

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1

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a b c

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a b + b c + c a

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Solution

The correct option is C $0$
$∣ ∣ ∣ ∣ \begin{matrix} 1 & b c & a b + a c 1 & c a & b a + b c 1 & a b & c a + c b \end{matrix} ∣ ∣ ∣ ∣$
$∣ ∣ ∣ ∣ \begin{matrix} 1 & b c & a b + b c + a c 1 & c a & a b + b c + c a 1 & a b & a b + b c + c a \end{matrix} ∣ ∣ ∣ ∣$
$= (a b + b c + c a) ∣ ∣ ∣ ∣ \begin{matrix} 1 & b c & 1 1 & c a & 1 1 & a b & 1 \end{matrix} ∣ ∣ ∣ ∣$
$= 0$

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