- #1
pyroknife
- 613
- 3
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?
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?