Lecture
This lecture covers Farkas' Lemma, which states that for a given matrix A, exactly one of two conditions holds: there exists a vector x > 0 such that Ax = b, or there exists a vector such that ATx > 0 and 1.5 < 0. The lecture then delves into certificates, hyperplane separation, and the application of Farkas' Lemma in combinatorics and game theory. In the context of game theory, the lecture explores how mixed strategies can be used to determine the probability of a goal in a penalty kick scenario, emphasizing the strategic decision-making process between the goalie and the striker.