Let \(A= [a_{ij}]_{1\leq i,j\leq 5}\) be a \(5\times 5\) positive definite (real) matrix. Show that the matrix \([a_{ij}/(i+j)]\) is also positive definite.
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Let \(A= [a_{ij}]_{1\leq i,j\leq 5}\) be a \(5\times 5\) positive definite (real) matrix. Show that the matrix \([a_{ij}/(i+j)]\) is also positive definite.