\begin{bmatrix}
1 & 2 & 3 \\
0 & 4 & 5 \\
0 & 0 & 6
\end{bmatrix}
An upper triangular matrix is a matrix where all elements "below" the main diagonal is zero. Alternatively, A matrix \(M\) is an upper triangular matrix if all elements \(m_{i j}\) is zero where \(i<j\).