Is the 0 matrix upper triangular? The reason I ask is because I'm trying to determine whether something is a subspace. The problem is determine whether the subset S of M2x2 is a subspace where S is the set of all upper triangular matrices. So these 3 must be satisfied: 1) 0 vector(matrix) is in S 2) if U and V are in S then U+V is in S 3) if V is in S, then cV where c is a scalar is in S if 0 matrix is in S then that means S= 0 0 0 0 But is that still upper triangular? Upper triangular is defined as having all entries below the main diagnol be 0. I thought a main diagonal was having a nonzero # along the diagonal?