Please help me with this question.

Problem F.3 (30 points) A doubly stochastic n X 71 matrix X : {raj} is a matrix such that the elements of each of its rows and columns are nonnegative, and sum to one. Thus the set of doubly stochastic matrices can be identied with the polyhedron 8 of R732 specied by the inequalities 3? S? ha . he. | || UH UH :5 a || H l' UH is :3 11735; 2 '0, VLj: 3...???\" A pcmutatz'on matrix is a doubly stochastic matrix Whose elements are either one or zero. (a) Show that the extreme points of S are the permutation matrices. (b) Verify that the matrix specifying the polyhedron 8 is totally unimodular. (c) Show that every doubly stochastic matrix X can be written as 229:1 71X; Where X; . . k are permutation matrices and g > 0, 21.21 73' : 1