Problem 4. Suppose that A in an m x n matrix and b is a vector...

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Problem 4. Suppose that A in an m x n matrix and b is a vector in R. Let a = (a1,..., am) be a vector in Rm. Carefully prove that the following two statements are equivalent: There is a vector x R" such that Ax = b and x > 0. The linear program Wa++am = Minimize subject to Ax + Ia = b x0, a0 has a feasible solution with W* = 0. Problem 4. Suppose that A in an m x n matrix and b is a vector in R. Let a = (a1,..., am) be a vector in Rm. Carefully prove that the following two statements are equivalent: There is a vector x R" such that Ax = b and x > 0. The linear program Wa++am = Minimize subject to Ax + Ia = b x0, a0 has a feasible solution with W* = 0.