Problem 20. Farkas' theorem tells us the following. Let A be an mxn matrix over R and c be an n-vector in R". Then exactly one of the following systems has a solution: System 1: Ax < 0 and c™x > 0 for some x € R". System 2: ATy = c and y > 0 for some y € R". Let (!) 1 0 1 0 1 0 1 0 1 A = c = 1 Find out whether system (1) or system (2) has a solution.

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