1. Let's recall that a matrix is lower triangular if all entries above the main diagonal are zero. 2. For matrix (a): $$\begin{pmatrix} 2 & 0 & 0 & 0 \\ 11 & 2 & 0 & 0 \\ 3 & -4 & 7 & 0 \\ 7 & 5 & -8 & 6 \end{pmatrix}$$ Check the entries above the main diagonal (positions where column index > row index): - (1,2) = 0, (1,3) = 0, (1,4) = 0 - (2,3) = 0, (2,4) = 0 - (3,4) = 0 All these are zero, so matrix (a) satisfies the condition. 3. For matrix (b): $$\begin{pmatrix} 11 & 4 & -2 \\ 0 & -13 & 7 \\ 0 & 0 & -8 \end{pmatrix}$$ Check the entries above the main diagonal: - (1,2) = 4 (not zero), (1,3) = -2 (not zero) - (2,3) = 7 (not zero) Since these are not zero, matrix (b) is not lower triangular. 4. From the above checks, matrix (a) is lower triangular, matrix (b) is not. Final answer: Matrix (a) is lower triangular, matrix (b) is not.