Subjects linear algebra

Upper Triangular

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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.