Minor of a matrix :
Let |A| = |[a ij]| be a determinant of order n.
The minor of an arbitrary element a_{ij} is the determinant obtained by deleting the i^{th} row and j^{th} column in which the element a_{ij} stands. The minor of a_{ij} by M_{ij}.
Cofactors :
The co factor is a signed minor. The cofactor of a_{ij} is denoted by A_{ij} and is defined as
A_{ij} = (-1)^{(i+j)} M_{ij}
Problem 1 :
Find the minor and cofactor of the following matrix.
Solution :
Problem 2 :
Find the minor and cofactor of the following matrix.
Solution :
Minor of a_{11} = 4-3 ==> 1
Minor of a_{12} = 4-2 ==> 2
Minor of a_{13} = 3-2 ==> 1
Minor of a_{21} = 8-9 ==> -1
Minor of a_{22} = 4-6 ==> -2
Minor of a_{23} = 3-4 ==> -1
Minor of a_{31} = 2-3 ==> -1
Minor of a_{32} = 1-3 ==> -2
Minor of a_{33} = 1-2 ==> -1
Problem 3 :
Find the minor and cofactor of the following matrix.
Solution :
Minor of a_{11} = 4-3 ==> 1
Minor of a_{12} = 12-10 ==> 2
Minor of a_{13} = 9-10 ==> -1
Minor of a_{21} = 8-3 ==> 5
Minor of a_{22} = 24-10 ==> 14
Minor of a_{23} = 18-20 ==> -2
Minor of a_{31} = 2-1 ==> 1
Minor of a_{32} = 6-3 ==> 3
Minor of a_{33} = 6-6 ==> 0
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