# Linear Algebra/Cofactors and Minors

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## Cofactors[edit]

Consider any column, the k^{th} one. Consider all terms that contain the element a_{ik}, and factor out a_{ik}. The sum of all such terms is called the cofactor of a_{ik}, do be denoted Co(a_{ik}).

Every term contains exactly one element from the k^{th} column. A determinant D can thus be written as a_{1k}Co(a_{1k})+a_{2k}Co(a_{2k})+a_{3k}Co(a_{3k})+...a_{nk}Co(a_{nk}).

If, in fact the cofactors of a column or row were to be multiplied by some different column and row, its sum would be zero because it would be the same as a determinant with repeat columns and rows.