Question: 2. For a given matrix A , show that the following two statements are equivalent: A x 0 and x 0 implies that x 1

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

  1. Ax 0 and x 0 implies that x1 = 0.
  2. There exists some vector p 0 such that pTA 0, and pTA1< 0 (strict inequality), where A1 denotes the first column of A.

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