Unlock the power of linear algebra with our Cofactor Expansion Calculator. Easily compute the determinant of any square matrix using this fundamental method. Perfect for students and professionals, it simplifies complex matrix operations and helps you understand the underlying mathematical principles.
Formula:
The determinant of a matrix A using cofactor expansion along row i is given by:
det(A) = Σj=1n (-1)i+j · aij · Mij
Where:
- aij: The element in the i-th row and j-th column.
- Mij: The minor, which is the determinant of the submatrix formed by removing the i-th row and j-th column.
- (-1)i+j: Determines the sign of the cofactor for element aij.
For a 3x3 matrix A = [[a, b, c], [d, e, f], [g, h, i]], det(A) = a(ei - fh) - b(di - fg) + c(dh - eg).