Upper Triangular
1. The problem asks which of the given matrices are upper triangular.
2. Recall that an upper triangular matrix is a square matrix where all elements below the main diagonal are zero.
3. Examine matrix (a):
$$\begin{pmatrix} 2 & 0 & 0 & 0 \\
11 & 2 & 0 & 0 \\
3 & -4 & 7 & 0 \\
7 & 5 & -8 & 6 \end{pmatrix}$$
Elements below the main diagonal include 11, 3, 7, -4, 5, -8 which are not zero.
Therefore, matrix (a) is **not** upper triangular.
4. Examine matrix (b):
$$\begin{pmatrix} 11 & 4 & -2 \\
0 & -13 & 7 \\
0 & 0 & -8 \end{pmatrix}$$
All elements below the main diagonal are zero.
Therefore, matrix (b) **is** upper triangular.
5. Conclusion: Matrix (b) is upper triangular, but matrix (a) is not.