Determinants — Chapter Summary

The determinant of a square matrix

The determinant of a square matrix A is a unique expression or number associated with A. It is written as det A or |A|. Only square matrices have dete

For a 1 x 1 matrix

For a 1 x 1 matrix [a11], the determinant is a11. For a 2 x 2 matrix [[a11, a12], [a21, a22]], |A| = a11a22 - a21a12. For a 3 x 3 matrix, the determin

The minor Mij of the (i

The minor Mij of the (i, j)th element is the determinant obtained after deleting the ith row and jth column of a square matrix. For an order-n matrix,

The cofactor of the (i

The cofactor of the (i, j)th element is Cij = (-1)^(i+j) Mij. The sign changes according to position in the matrix.

The determinant equals the sum

The determinant equals the sum of the products of the elements of any row or column with their corresponding cofactors.