Question: Please look at picture below (3) For each k E N, define the set Be to be the collection of all k x k matrices

Please look at picture below

(3) For each k E N, define the set Be to be the collection of all k x k matrices with nonnegative entries whose rows and columns each sum to one. For example, 1 12 | xy 2 0 for i, j = 1, 2 , 21 + 212 = 1, $21 + 122 = 1, THI + 121 = 1, 212 + 122 = 1}. B2 = 1 121 T22 Prove that B2 is a convex polytope. Hint: What are the extreme points of B2

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