MathDB

For a matrix

(p_{ij})

of the format

m\times n

with real entries, set

a_i =\displaystyle\sum_{j=1}^n p_{ij}\text{ for }i = 1,\cdots,m\text{ and }b_j =\displaystyle\sum_{i=1}^m p_{ij}\text{ for }j = 1, . . . , n\longrightarrow(1)

By integering a real number, we mean replacing the number with the integer closest to it. Prove that integering the numbers

a_i, b_j, p_{ij}

can be done in such a way that

(1)

still holds.

Problem Statement