Question: For a given matrix A, show that following two statements are equivalent: (i) Ax >= 0 and x >= 0 implies that x 1 =

For a given matrix A, show that following two statements are equivalent:

(i) Ax >= 0 and x >= 0 implies that x1 = 0

(ii) There exists some vector p >= 0 s.t. pT A <= 0, and pT A1 <0 (strict inequality), where a1 denotes the first column of A.

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