Question

Give an example of an upper triangular matrix.

Answer 1

Hint: A square matrix with all elements equal to zero below the main diagonal is an upper triangular matrix.

An upper triangular matrix is a triangular matrix with all elements equal to below the main diagonal. It is a square matrix with element ${{\text{a}}_{{\text{ij}}}}$ where ${{\text{a}}_{{\text{ij}}}}$ = 0 for all j < i.
Example of a $2 \times 2$matrix.
\left( {\begin{array}{*{20}{c}} 1&2 \\\ 0&3 \end{array}} \right)
Example of a $3 \times 3$matrix
\left( {\begin{array}{*{20}{c}} 8&9&7 \\\ 0&7&5 \\\ 0&0&4 \end{array}} \right)

Note: The upper triangular matrices are strictly square matrices. On adding or multiplying two upper triangular matrices, the resultant matrix is also the upper triangular matrix.