Cofactor Matrix Confusion: Solving for Minor Determinants

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Wminus
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Here's a problem I am doing right now.
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What are the cofactors " ## \Delta_{i \alpha} ##"? I know they are represent the minor of some determinant, but I am confused and can't see which determinant it is.

Also, could somebody please help me and explain why ## ( V_{ij} - \omega^2 T_{ij} ) \Delta_{i \alpha}##?

Thanks
 

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