I was reading about farkas-minkowski theorem, which basically said a convex cone is polyhedral iff it's finitely generated. The theorem make sense, but when I played with some example I met the following problem:
If my cone is
$$\mathrm{cone}\{(1,2),(2,4)\} = \{ \lambda_1 (1,2)+ \lambda_2 (2,4)\mid\lambda_1, \lambda_2 \geq 0\}$$
Which is a silly but finitely genarated cone.
And the definition of ployhedral cone is $C = \{ x \mid Ax \leq 0 \}$ for some matrix $A$
My question is what's the matrix $A$ of this cone? And what's a general strategy to find such matrix if the given cone is finitely generated.
Any help would be appreciated!