Answer to Question #25748 in Abstract Algebra for john.george.milnor

Question

Let R be a simple ring with center k (which is a field). Let x1, . . . , xn ∈ R be linearly independent over k. Show that, for any y1, . . . , yn ∈ R, there exist a1, . . . , am and b1, . . . , bm in R such that yi = (sum over j) ajxibj for every i.