Question

(i) Let f : V → F be a linear map. Prove that the set {v ∈ V | f(v) = 0} is a subspace of V

(ii) Using Part (i), show that the subset W of V = M_n(F) consisting of matrices A = [aij ]1≤i,j≤n with Sum_1≤i≤n aii = 0 is a subspace of V .