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Find the mino...

Question

Find the minor of element $6$ in the determinant
$Δ = ∣ ∣ ∣ ∣ \begin{matrix} 1 & 2 & 3 4 & 5 & 6 7 & 8 & 9 \end{matrix} ∣ ∣ ∣ ∣$

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Solution

Given: $Δ = ∣ ∣ ∣ ∣ \begin{matrix} 1 & 2 & 3 4 & 5 & 6 7 & 8 & 9 \end{matrix} ∣ ∣ ∣ ∣$
Since $6$ lies in the second row and third column i.e. $a_{23} = 6$
Minor of $a_{23} = M_{23} = ∣ ∣ ∣ ∣ \begin{matrix} 1 & 2 & 3 4 & 5 & 6 7 & 8 & 9 \end{matrix} ∣ ∣ ∣ ∣$
$= ∣ ∣ ∣ \begin{matrix} 1 & 2 7 & 8 \end{matrix} ∣ ∣ ∣ = 8 - 14 = - 6$
Thus, minor of element $6$ is $- 6$ .

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