I want to reduce the vertex cover problem to a specific decision problem. This decision problem is the following:
I have a nxn matrix A, a vector b in R^n, and a positive integer k. Does there exists a vector x in R^n with at most k non-zero entries such that A*x is greater than or equal to b?
I was thinking that A could be viewed as an adjacency matrix, but I'm not sure how to reduce the vertex cover problem to this problem.
Can anyone give me a hint or two on what I should do next?
EDIT**I originally thought about using dominating set problem, but after thinking through the problem a little more, I thought I should use vertex cover instead. (so question originally referred to dominating set)