Xét ma trận

B = [ 1 2 3 4 5 6 7 8 9 ] . {\displaystyle B={\begin{bmatrix}1&2&3\\4&5&6\\7&8&9\end{bmatrix}}.}

Khai triển Laplace theo hàng đầu tiên:

| B | = 1 ⋅ | 5 6 8 9 | − 2 ⋅ | 4 6 7 9 | + 3 ⋅ | 4 5 7 8 | = 1 ⋅ ( − 3 ) − 2 ⋅ ( − 6 ) + 3 ⋅ ( − 3 ) = 0. {\displaystyle {\begin{aligned}|B|&=1\cdot {\begin{vmatrix}5&6\\8&9\end{vmatrix}}-2\cdot {\begin{vmatrix}4&6\\7&9\end{vmatrix}}+3\cdot {\begin{vmatrix}4&5\\7&8\end{vmatrix}}\\[5pt]&=1\cdot (-3)-2\cdot (-6)+3\cdot (-3)=0.\end{aligned}}}

Khai triển Laplace theo cột thứ hai:

| B | = − 2 ⋅ | 4 6 7 9 | + 5 ⋅ | 1 3 7 9 | − 8 ⋅ | 1 3 4 6 | = − 2 ⋅ ( − 6 ) + 5 ⋅ ( − 12 ) − 8 ⋅ ( − 6 ) = 0. {\displaystyle {\begin{aligned}|B|&=-2\cdot {\begin{vmatrix}4&6\\7&9\end{vmatrix}}+5\cdot {\begin{vmatrix}1&3\\7&9\end{vmatrix}}-8\cdot {\begin{vmatrix}1&3\\4&6\end{vmatrix}}\\[5pt]&=-2\cdot (-6)+5\cdot (-12)-8\cdot (-6)=0.\end{aligned}}}