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displaystyle \mathbf {y} \in \mathbb {r} ^{m}} such that a t y ≥ {\displaystyle \mathbf {a} ^{\mathsf {t}}\mathbf {y} \geq } and b t y , b = b − b, so: b y + b y = b y + b y − b y = b ( y + y ) / − b y . thus we can take, for example, y = , y = − . geometric interpretation[ edit ] consider the closed convex cone
i = , ... , n {\displaystyle i= ,\dots ,n} , and b t y < {\displaystyle \mathbf {b} ^{\mathsf {t}}\mathbf {y} < } . the sums x a + ⋯ + x n a n {\displaystyle x_{ }\mathbf {a} _{ }+\dots +x_{n}\mathbf {a} _{n}} with nonnegative coefficients x , ... , x n {\displaystyle x_{ },\dots ,x_{n}} form the cone...
https://en.wikipedia.org/wiki/Farkas%27_lemma