- #1
Buffu
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Homework Statement
Find the inverse of
##A = \begin{bmatrix} 1 & \dfrac12 & & \cdots && \dfrac1n
\\\dfrac12 & \dfrac13 && \cdots && \dfrac1{n+1}
\\ \vdots & \vdots && && \vdots
\\ \dfrac1n & \dfrac1{n+1} && \cdots && \dfrac1{2n-1}\end{bmatrix}##
Homework Equations
The Attempt at a Solution
I obvserved that ##A_{ij} = \dfrac{1}{i+j-1}##.Also I know ##I = AA^{-1}##
So jth column of ##I## is ##A## times jth column of ##A^{-1}##
So for ##j = 1##
##A \times \begin{bmatrix}A^{-1}_{11} \\ \vdots \\ A^{-1}_{n1}\end{bmatrix} = \begin{bmatrix} 1 \\ 0 \\ \vdots\\0 \end{bmatrix}##.
Now I don't know what to do. Any clue.