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Let S be the set of all points (x1,,xn) in Rn that satisfy all the m inequalities a11x1+a12x2++a1nxnb1a21x1+a22x2++a2nxnb2am1x1+am2x2++amnxnbm and moreover are such that x10,,xn0. Show

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Let S be the set of all points (x1,,xn) in Rn that satisfy all the m inequalities a11x1+a12x2++a1nxnb1a21x1+a22x2++a2nxnb2am1x1+am2x2++amnxnbm and moreover are such that x10,,xn0. Show that S is a convex set

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