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An application of linear algebra in Calculus

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Posted on: March 24, 2019

Definition. For an integer $latex n ge 1,$ the $latex ntimes n$ Hilbert matrix is defined by $latex H_n=[a_{ij}],$ where $latex displaystyle a_{ij}=frac{1}{i+j-1},   1 le i,j le n.$ It is known that $latex H_n$ is invertible and if $latex H_n^{-1}=[b_{ij}],$ then $latex displaystyle sum_{i,j}b_{ij}=n^2.$ We are going to use these two properties of…