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4
votes
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What is the inverse of a triangular matrix whose nonzero elements are binomial coefficients?...
Let
\begin{equation*}
\begin{split}
M_m
&=\begin{pmatrix}
-\binom{1}{0} & \binom{2}{0} &-\binom{3}{0} &\dotsm & (-1)^{m-1}\binom{m-1}{0} & (-1)^m\binom{m}{0}\\
0 & \binom{2}{1} &-\binom{3}{1} &\dotsm …