Thread: restriction

let f: V--> W , g:U--> V be linear maps of finite dim vector spaces. let U_1= ker(fg) and V_1 = ker(f). show that g restricts to a linear map g_1 :U_1--> V_1 and that ker(g) = ker(g_1).

im not even sure hot to begin solving this question. ..
im wondering, why would the ker(f)= V_1 be the codomain where g_1 maps U_1 into.

U1 is defined as ker(fg). That is, if u is in U1, f(g(u))= 0. If we let v= g(u), that says that f(v)= 0 so that v is in ker(f). That is, for u in U1, g(u)= v is in ker(f).

what does it mean by g restricts to a linear map g1?

i know that the ker(g_1) is the dim of U_1 right?

i still dont really know how to solve it..hmm