Determinant
Defined only for square matrices. Denoted by
For 2x2
For higher order
Minor of an element
Suppose
Minor of an element
Co-factor of an element
Suppose
Co-factor of an element
Definition
If
where
Properties of determinants
- Every element of a row or column of a matrix is
then the value of its determinant is . - If 2 columns or 2 rows of a matrix are identical then its determinant is
. - If A and B are two square matrices then
. - The value of the determinant of a matrix remains unchanged if a scalar multiple of a row or column is added to any other row or column.
- If a matrix
is obtained from a square matrix by an interchange of two columns or rows: . - If every entry in any row or column is multiplied by
, then the whole determinant is multiplied by .
In relation with eigenvalues
For a