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.
$\left(\begin{array}{cc}1& 2\\ 0& 3\end{array}\right)$
Example of a $3\times 3$matrix
$\left(\begin{array}{ccc}8& 9& 7\\ 0& 7& 5\\ 0& 0& 4\end{array}\right)$

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.