How to Calculate Matrix of Minor and Co-factor?

Matrix of Minor and Co-factor - Definition and Example

Definition:

The co-factors of the matrix are basically used to find the adjoint of the matrix and inverse of the matrix.

Matrix of Minors:

For each element of the matrix do follow steps

1. Ignore the values on the current row and column

2. Calculate the determinant of the remaining values

Matrix of Cofactor

Change the sign of alternate cells is known to be Matrix of Cofactor.

Example :

Find minor and cofactor of Matrix for following Matrix

1 -2 3
0 5 1
2 -1 0
Given :
1 -2 3
0 5 1
2 -1 0

Solution :

Matrix of Minor:
(5x0)-(1x-1) (0x0)-(1x2) (0x-1)-(5x2)
(-2x0)-(3x-1) (1x0)-(3x2) (1x-1)-(-2x2)
(-2x1)-(3x5) (1x1)-(3x0) (1x5)-(-2x0)
0+1 0-2 0-10
0+3 0-6 -1+4
-2-15 1-0 5-0
1 -2 -10
3 -6 3
-17 1 5
Matrix of Cofactor:
1 -1x-2 -10
-1x3 -6 -1x3
-17 -1x1 5
1 2 -10
-3 -6 -3
-17 -1 5

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