Questions & Answers

Give an example of an upper triangular matrix.

Answer Verified Verified
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.
$\left( {\begin{array}{*{20}{c}}
  1&2 \\
\end{array}} \right)$
Example of a $3 \times 3$matrix
$\left( {\begin{array}{*{20}{c}}
  8&9&7 \\
  0&7&5 \\
\end{array}} \right)$

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.
Bookmark added to your notes.
View Notes