The online calculator calculates symbolic the value of the determinant of a 5x5 matrix after Sarrus rule and with the Laplace expansion in a row or column.
Enter the coefficients
Brackets has to be set explicit. Not a+b but (a+b) is ok.
Calculation using the Laplace expansion
You can select the row or column to be used for expansion.
Laplace Expansion Theorem
The Laplacian development theorem provides a method for calculating the determinant, in which the determinant is developed after a row or column. The dimension is reduced and can be reduced further step by step up to a scalar.
where Aij, the sub-matrix of A, which arises when the i-th row and the j-th column are removed.
Example of the expansion according to the j-th row of a NxN determinant.
The Laplace expansion reduces the NxN determinant to a sum of (N-1)x(N-1) determinants.