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Problem 6 (due Monday, April 27)
Let M be an m×n matrix whose entries are positive real numbers. For each column of M compute the product of all the numbers in that column. Let S(M) be the sum of all these products. Now let N be the matrix obtained form M by putting entries in each row in a non-decreasing order. Prove that S(N)≥S(M).
This problem was solved by only one participant: Yuqiao Huang. The submitted solution is correct and similar to our original solution, but a justification of a key claim is missing. Detailed solution is discussed in the following link Solution