I've a problem, I have to find a vector v=[vx vy]' (column) such that:
where y=[y1 y2] (row) and x,y1,y2,vx,vy are a real scalar.
Does anyone know an analytic solution?
Your equation can be written as vx*y1 + vy*y2 < x.
There are many solutions (unless y1=y2=0 and x<=0). In the general case, you can freely choose one component, for example vx=0. The remaining inequality vy*y2<x is satisfied for vy = x/y2 -1, assuming y2 !=0.