linear programming proofs

i have these two questions that i am having trouble understanding.

1. show that the linear kuhn-tucker theorem implies the complementary slackness conditions.

2. show that if A is a linear transformation and A' is the dual transformation, then the matrices of A and A' in the standard bases are transposes of each other.

i'm not sure if i'm understanding what the linear kuhn-tucker theorem is saying, because i have found many versions of it, but none of them were comprehensible for me.