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If $A=(a_{ij})$ is a real positive definite symmetric matrix of order $n$. How to show $(n-1)\prod_{i=1}^na_{ii}+\det A\ge \sum_{i=1}^na_{ii}\det A(i)$? $A(i)$ means the submatrix of $A$ by deleting the $i$th row and $i$th column.

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