Question: Let M be an n1 n2 matrix such that each entry M(i, j) is a non-negative real number where the sum of each row and

Let M be an n1 n2 matrix such that each entry M(i, j) is a non-negative real number where the sum of each row and each column is an integer. Using the max-flow min-cut theorem, prove that there must exists an n1 n2 matrix N such that each entry N(i, j) is a non-negative integer and the sum of each row and each column is identical to that for M.

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