Question: 2.For a given matrix A, show that the following two statements are equivalent: (i)Ax ? 0 and x ? 0 implies that x? = 0.

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

(i)Ax ? 0 and x ? 0 implies that x? = 0.

(ii)There exists some vector p ? 0 such that pTA ? 0, and p A?

See attached.

2. For a given matrix A, show that the following two statements are equivalent: (i) A56 2 0 and m 2 0 implies that 331 : 0. (ii) There exists some vector p 2 0 such that pTA g 0, and pTAl

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