Prove that every linear map from Fn,1\mathbf F^{n,1}Fn,1 to Fm,1\mathbf F^{m,1}Fm,1 is given by a matrix multiplication. In other words, prove that if T∈L(Fn,1,Fm,1)T \in \mathcal L(\mathbf F^{n,1}, \mathbf F^{m,1})T∈L(Fn,1,Fm,1), then there exists an mmm-by-nnn matrix AAA such that Tx=AxTx = AxTx=Ax for every x∈Fn,1x \in \mathbf F^{n,1}x∈Fn,1.
TODO