Laplace formula is the most widely used formula to calculate the determinant a square matrix.
Minor of a Matrix :
Co-factor of a matrix :
Co-factor expansion (Laplace expansion) :
Calculate the determinant of a general 3 × 3 matrix
Let A =
Task :
First let us discuss the symbols and terms used in Leibniz formula.
Symmetric group Sn :
Odd and even permutations :
Signature function sgn() :
Leibniz formula for determinant :
Task :
Levi-Citiva symbol : εi1 i2 i3 .... in
Calculate using Levi-Civita formula.
Let us first determine ε11, ε12, ε21, ε22
Task :