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Determinants

Question

Find the minor of the element of second row and third column ( a₂₃ ) in the following determinant:
$|\begin{matrix} 2 & - 3 & 5 \\ 6 & 0 & 4 \\ 1 & 5 & - 7 \end{matrix}|$

Solution

Given determinant = $|\begin{matrix} 2 & - 3 & 5 \\ 6 & 0 & 4 \\ 1 & 5 & - 7 \end{matrix}|$

Minor of the element a₂₃ is M₂₃

Obtained by deleting III column and II row

$M_{23} = |\begin{matrix} 2 & - 3 \\ 1 & 5 \end{matrix}| = 10 - (- 3) = 13$