Given the equality of the following determinants. Find the value of $(a + b)$ .
$∣ ∣ ∣ \begin{matrix} 4 & 3 6 & a \end{matrix} ∣ ∣ ∣ = ∣ ∣ ∣ \begin{matrix} 6 & b 4 & 5 \end{matrix} ∣ ∣ ∣$

8

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12

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14

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16

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Solution

The correct option is B $12$
Given :
$∣ ∣ ∣ \begin{matrix} 4 & 3 6 & a \end{matrix} ∣ ∣ ∣ = ∣ ∣ ∣ \begin{matrix} 6 & b 4 & 5 \end{matrix} ∣ ∣ ∣$
$⟹$ $4 a - 6 \times 3 = 6 \times 5 - 4 b$
$⟹$ $4 a + 4 b = 30 + 18$
$⟹$ $4 (a + b) = 48$
$⟹$ $a + b = 12$
Hence, option B is correct.

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