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