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.