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Determinants

Question

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Find the co-factor of a12 in the following:
$|\begin{matrix} 2 & - 3 & 5 \\ 6 & 0 & 4 \\ 1 & 5 & - 7 \end{matrix}|$

Solution

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

Cofactor of a₁₂ = ( -1 )¹⁺² [ 6(-7) - 4(1) ]

= (-1) [ -42 - 4 ]

= 46

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