Sum of minor and co-factor of element 2020 of | vedclass

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(B) Let the determinant be $\Delta = \begin{vmatrix} a_{11} & a_{12} & a_{13} \ a_{21} & a_{22} & a_{23} \ a_{31} & a_{32} & a_{33} \end{vmatrix}$.T

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(B) Let the determinant be $\Delta = \begin{vmatrix} a_{11} & a_{12} & a_{13} \ a_{21} & a_{22} & a_{23} \ a_{31} & a_{32} & a_{33} \end{vmatrix}$.The element $2020$ is at the position $a_{12}$ (first row,second column).The minor $M_{12}$ is the determinant of the $2 	imes 2$ matrix obtained by deleting the first row and second column:$M_{12} = \begin{vmatrix} 2022 & 2024 \ 2025 & 2027 \end{vmatrix} = (2022 	imes 2027) - (2024 	imes 2025)$.Using the property $(x-a)(x+a) = x^2 - a^2$ or direct calculation:$M_{12} = (2024.5 - 2.5)(2024.5 + 2.5) - (2024.5 - 0.5)(2024.5 + 0.5) = (2024.5^2 - 6.25) - (2024.5^2 - 0.25) = -6.25 + 0.25 = -6$.Alternatively,$M_{12} = (2022 	imes 2027) - (2024 	imes 2025) = 4098594 - 4098600 = -6$.The co-factor $C_{12} = (-1)^{1+2} M_{12} = -1 	imes (-6) = 6$.The sum of the minor and the co-factor is $M_{12} + C_{12} = -6 + 6 = 0$.

Sum of minor and co-factor of element $2020$ of $\Delta=\left|\begin{array}{rrr}2019 & 2020 & 2021 \\ 2022 & 2023 & 2024 \\ 2025 & 2026 & 2027\end{array}\right|$ is . . . . . . .

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