Can I use linprog to solve for the vector k

I should obtain a vector k=[k1,k2,....,kn], here k1,k2..kn are vectors.

F is a 3*1 wrench matrix (where it contains the momenta,force along x,force along y).

So, I should obtain a vector k such that

(k1*F1)+(k2*F2).....+(k8*F8) +X =0;

(k8*F8)+(k9*F9).....+(k16*F16) +Y =0;

(k5*F5)+....(k12*F12)+Z=0;

The matrices F1,F2,...,F16, X,Y,Z are all known.

Well, the question would be striaght-forward had the last equation not been there, but here k5,k6,..,k12 repeats!