How about the linear map which takes every element of V to the 0 element of W. Then if you let U be the subspace with only the 0 element of V. then and
Hi, i'm having trouble starting this proof and how to prove the ideas necessary.
Let V and W be finite-dimensional vector spaces over F. Given T is in L(V,W), show that there is a subspace U of V such that the following are true:
U(intersection)null(T)= {0} and range(T)={Tu:u in U}.
Thank you