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## Homework Statement

If dim(X)=n, show that the vector space of k-linear forms on X is of dimension n

^{k}.

## Homework Equations

## The Attempt at a Solution

So I know we need to let x

_{1}, x

_{2,}...x

_{n}be a basis for X. My professor then said to "show that the function f

_{j1,...,jk}, 1≤j

_{l}≤n defined by f

_{j1,...,jk}(x

_{i1,}...x

_{ik}) = δ

_{i1j1},...,δ

_{ikjk}and then extend multilinearly." This is where I am lost on what to do. Any help would be much appreciated.