HOW TO FIND MINORS AND COFACTORS OF A MATRIX

Minor of a Matrix :

Let |A| = |[a ij]| be a determinant of order n.

The minor of an arbitrary element aij is the determinant obtained by deleting the ith row and jth column in which the element aij stands. The minor of aij by Mij.

Cofactors :

The co factor is a signed minor. The cofactor of aij is denoted by Aij and is defined as

Aij  =  (-1)(i+j) Mij

Example 1 :

Find the minor and cofactor of the following matrix

Solution :

Minor of a11 (Ignore 1st row and 1st column)

Minor of a11  =  -6+4  ==>  -2

Minor of a12  =  0-10  ==>  -10

Minor of a13  =  0+5  ==>  5

Minor of a21  =  24+2  ==>  26

Minor of a22  =  18-5  ==>  13

Minor of a23  =  -6-20  ==>  -26

Minor of a31  =  8+1  ==>  9

Minor of a32  =  6-0  ==>  6

Minor of a33  =  -3-0  ==>  -3 

Example 2 :

Find the minor and cofactor of the following matrix

Solution :

Minor of a11  =  2-0  ==>  2

Minor of a12  =  -2-0  ==>  -2

Minor of a13  =  4+2  ==>  6

Minor of a21  =  -1+2  ==>  1

Minor of a22  =  -3+1  ==>  -2

Minor of a23  =  6-1  ==>  5

Minor of a31  =  0-2  ==>  -2

Minor of a32  =  0+2  ==>  2

Minor of a33  =  -6-2  ==>  -8 

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