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Show that for any matrix \(A \in \Rmm\text{,}\)
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\begin{equation*}
\|A\|_\infty = \max_{i=1, \dots, m} \sum_{j=1}^m |a_{i,j}|.
\end{equation*}
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\begin{equation*}
\|A\|_1 = \max_{j=1, \dots, m} \sum_{i=1}^m |a_{i,j}|.
\end{equation*}
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