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?
May be these aj,k = 0 for all j > k and A = AT
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.