Hi! Have some troubles with solving one problem in my assignment, would be great if somebody could help me. The problem is following:

Letn>0and letL_{n,k }, whear1<=k<=nbe a subspace spanned by vectorsefor_{j}j=1...k. Show that it exist a linear transformation T:R^{n}=>R^{(n-k)}such as L_{n,k}=Ker(T)