Difference between revisions of "1971 IMO Problems/Problem 6"
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Let A = (
Let A = ()i, j = 1, 2, , nbe a square matrix non-negative integers. that = 0, the sum of the elements in the row and the column is n. Prove that the sum of all the elements the matrix is / 2.
Revision as of 14:10, 29 January 2021
Let be a square matrix whose elements are non-negative integers. Suppose that whenever an element , the sum of the elements in the th row and the th column is . Prove that the sum of all the elements of the matrix is .