VINOD A V,
PGT Mathematics,
Jawahar Navodaya Vidyalaya,
Thrissur-KERALA
DETERMINANTS
Determinant of a matrix of order one
Let A = [a] be the matrix of order 1, then determinant of A is defined to be equal to a.
Determinant of a matrix of order two
Example
Determinant of a matrix of order two
Determinant of a matrix of order three can be determined by expressing it in terms of second order determinants. This is known as expansion of a determinant along a row (or a column).
Determinant of a matrix of order 3
Step 4
Now the expansion of determinant of A, that is, | A | written as sum of all three terms obtained in steps 1, 2 and 3 above is given by
Example
MINORS AND COFACTORS
Minor of an element
To each element of a square matrix, a number called its minor is associated.
The minor of an element is the value of the determinant obtained by deleting the row and column containing the element.
Examples:
Remark Minor of an element of a square matrix of order n(n ≥ 2) is a determinant of
order n – 1.
Cofactor of an element
Minors and Cofactors
Note:-
Example