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Determinants

Example 8

Find the minor of element 6 in the determinant \(\Delta=|\begin{smallmatrix}1&2&3\\ 4&5&6\\ 7&8&9\end{smallmatrix}|\)

Solution

Since 6 lies in the second row and third column, its minor \(M_{23}\) is given by \(M_{23}=|\begin{smallmatrix}1&2\\ 7&8\end{smallmatrix}|=8-14=-6\) (obtained by deleting \(R_{2}\) and \(C_{3}\) in A).