If the matrix
in (1) is a square matrix, then we associate with
a number denoted by
![]()
called the determinant of
of order n, written det(A). In order to define the value of a determinant, we introduce the following concepts.
Contents hide1. Minor
Given any element
of
we associate a new determinant of order (n – 1) obtained by removing all elements of the jth row and kth column called the minor of
.
2. Cofactor
If we multiply the minor of
by
, the result of the elements in any row [or column] by their corresponding cofactors and is called the Laplace expansion. In symbols,
![]()
We can show that this value is independent of the row [or column] used.
Determinants
