Determine whether the subset S of M2x2 (2x2 are the subscripts for M, idk how to do put it on here) is a subspace. Let S be the set of all diagonal matrices. To check if something is a subspace, my teacher gave us 3 conditions. 1.) 0 vector is in S 2) if U and V are in S, then U+V is in S 3) If V is in S and c is a scalar, then cV is in S. I'm not really sure how to check the first condition. A guess no vectors on a diagnol 2x2 matrix can be the 0 vector,thus S is not a subspace in this case?