1. The problem statement, all variables and given/known data This question is taken from Linear Algebra Done Wrong by Treil. Question 7.5 of chapter 1 says this: What is the smallest subspace of the space of 4 4 matrices which contains all upper triangular matrices (aj,k = 0 for all j > k), and all symmetric matrices (A = AT )? What is the largest subspace contained in both of those subspaces? 2. Relevant equations May be these aj,k = 0 for all j > k and A = AT 3. The attempt at a solution I'm just not sure with my answer because it sounds too short for such an elaborate question. 1st answer: the zero matrix, the one with all-zero entries. 2nd answer: the two subspaces themself.