原始行列式：
| 5 | 2 | 0 | 0 | 0 |
| 3 | 2 | 0 | 0 | 0 |
| 9 | 2 | 1 | 2 | 3 |
| 8 | 1 | 1 | 3 | 4 |
| 5 | 1 | 0 | 1 | 3 |
该行列式可以写成分块上三角形式：Δ = det [ A 0 ; C D ]，右上角为零矩阵，因此 Δ = det(A)·det(D)。
| 5 | 2 | 0 | 0 | 0 |
| 3 | 2 | 0 | 0 | 0 |
| 9 | 2 | 1 | 2 | 3 |
| 8 | 1 | 1 | 3 | 4 |
| 5 | 1 | 0 | 1 | 3 |
| 2 | 0 | 0 | 0 | 0 |
| 3 | 2 | 0 | 0 | 0 |
| 9 | 2 | 1 | 2 | 3 |
| 8 | 1 | 1 | 3 | 4 |
| 5 | 1 | 0 | 1 | 3 |
左上角 A 变为下三角矩阵，det(A) = 2×2 = 4。
| 2 | 0 | 0 | 0 | 0 |
| 3 | 2 | 0 | 0 | 0 |
| 9 | 2 | 1 | 2 | 3 |
| 8 | 1 | 1 | 3 | 4 |
| 5 | 1 | 0 | 1 | 3 |
| 2 | 0 | 0 | 0 | 0 |
| 3 | 2 | 0 | 0 | 0 |
| 9 | 2 | 1 | 0 | 3 |
| 8 | 1 | 1 | 1 | 4 |
| 5 | 1 | 0 | 1 | 3 |
| 2 | 0 | 0 | 0 | 0 |
| 3 | 2 | 0 | 0 | 0 |
| 9 | 2 | 1 | 0 | 3 |
| 8 | 1 | 1 | 1 | 4 |
| 5 | 1 | 0 | 1 | 3 |
| 2 | 0 | 0 | 0 | 0 |
| 3 | 2 | 0 | 0 | 0 |
| 9 | 2 | 1 | 0 | 0 |
| 8 | 1 | 1 | 1 | 1 |
| 5 | 1 | 0 | 1 | 3 |
| 2 | 0 | 0 | 0 | 0 |
| 3 | 2 | 0 | 0 | 0 |
| 9 | 2 | 1 | 0 | 0 |
| 8 | 1 | 1 | 1 | 1 |
| 5 | 1 | 0 | 1 | 3 |
| 2 | 0 | 0 | 0 | 0 |
| 3 | 2 | 0 | 0 | 0 |
| 9 | 2 | 1 | 0 | 0 |
| 8 | 1 | 1 | 1 | 0 |
| 5 | 1 | 0 | 1 | 2 |
主对角线元素为 2，2，1，1，2，故行列式值为：
同时，左上角二阶行列式 det(A) = 4，右下角三阶行列式 det(D) = 2，乘积也为：
分块行列式的值确实等于对角上那个二阶行列式和三阶行列式的乘积。