- Laplace's expansion is a method for finding the determinant of a matrix by breaking it down into smaller submatrices.
- The method involves selecting a row or column of the matrix, calculating the determinant of submatrices obtained by removing that row and column, and then multiplying each determinant by the corresponding element in the selected row or column.
- Laplace's expansion formula can be used recursively to calculate determinants of larger matrices by breaking them down into smaller submatrices.
- This method is not efficient for large matrices and other methods like Gaussian elimination or LU decomposition are preferred.
- Laplace's expansion is a useful tool in mathematics for solving problems that involve matrices
Formula $$|A| = \sum_{i=1}^{n} a_{ij} C_{ij} = \sum_{j=1}^{n} a_{ij} C_{ij}$$