1. The problem statement, all variables and given/known data If dim(X)=n, show that the vector space of k-linear forms on X is of dimension nk. 2. Relevant equations 3. The attempt at a solution So I know we need to let x1, x2,...xn be a basis for X. My professor then said to "show that the function fj1,...,jk, 1≤jl≤n defined by fj1,...,jk(xi1,...xik) = δi1j1,...,δikjk and then extend multilinearly." This is where I am lost on what to do. Any help would be much appreciated.