# Finite Math Examples

Find the Cofactor Matrix
Step 1
Consider the corresponding sign chart.
Step 2
Use the sign chart and the given matrix to find the cofactor of each element.
Step 2.1
Calculate the minor for element .
Step 2.1.1
The minor for is the determinant with row and column deleted.
Step 2.1.2
Evaluate the determinant.
Step 2.1.2.1
The determinant of a matrix can be found using the formula .
Step 2.1.2.2
Simplify the determinant.
Step 2.1.2.2.1
Simplify each term.
Step 2.1.2.2.1.1
Multiply by .
Step 2.1.2.2.1.2
Multiply by .
Step 2.1.2.2.2
Subtract from .
Step 2.2
Calculate the minor for element .
Step 2.2.1
The minor for is the determinant with row and column deleted.
Step 2.2.2
Evaluate the determinant.
Step 2.2.2.1
The determinant of a matrix can be found using the formula .
Step 2.2.2.2
Simplify the determinant.
Step 2.2.2.2.1
Simplify each term.
Step 2.2.2.2.1.1
Multiply by .
Step 2.2.2.2.1.2
Multiply by .
Step 2.2.2.2.2
Subtract from .
Step 2.3
Calculate the minor for element .
Step 2.3.1
The minor for is the determinant with row and column deleted.
Step 2.3.2
Evaluate the determinant.
Step 2.3.2.1
The determinant of a matrix can be found using the formula .
Step 2.3.2.2
Simplify the determinant.
Step 2.3.2.2.1
Simplify each term.
Step 2.3.2.2.1.1
Multiply by .
Step 2.3.2.2.1.2
Multiply by .
Step 2.3.2.2.2
Subtract from .
Step 2.4
Calculate the minor for element .
Step 2.4.1
The minor for is the determinant with row and column deleted.
Step 2.4.2
Evaluate the determinant.
Step 2.4.2.1
The determinant of a matrix can be found using the formula .
Step 2.4.2.2
Simplify the determinant.
Step 2.4.2.2.1
Simplify each term.
Step 2.4.2.2.1.1
Multiply by .
Step 2.4.2.2.1.2
Multiply by .
Step 2.4.2.2.2
Subtract from .
Step 2.5
Calculate the minor for element .
Step 2.5.1
The minor for is the determinant with row and column deleted.
Step 2.5.2
Evaluate the determinant.
Step 2.5.2.1
The determinant of a matrix can be found using the formula .
Step 2.5.2.2
Simplify the determinant.
Step 2.5.2.2.1
Simplify each term.
Step 2.5.2.2.1.1
Multiply by .
Step 2.5.2.2.1.2
Multiply by .
Step 2.5.2.2.2
Subtract from .
Step 2.6
Calculate the minor for element .
Step 2.6.1
The minor for is the determinant with row and column deleted.
Step 2.6.2
Evaluate the determinant.
Step 2.6.2.1
The determinant of a matrix can be found using the formula .
Step 2.6.2.2
Simplify the determinant.
Step 2.6.2.2.1
Simplify each term.
Step 2.6.2.2.1.1
Multiply by .
Step 2.6.2.2.1.2
Multiply by .
Step 2.6.2.2.2
Subtract from .
Step 2.7
Calculate the minor for element .
Step 2.7.1
The minor for is the determinant with row and column deleted.
Step 2.7.2
Evaluate the determinant.
Step 2.7.2.1
The determinant of a matrix can be found using the formula .
Step 2.7.2.2
Simplify the determinant.
Step 2.7.2.2.1
Simplify each term.
Step 2.7.2.2.1.1
Multiply by .
Step 2.7.2.2.1.2
Multiply by .
Step 2.7.2.2.2
Subtract from .
Step 2.8
Calculate the minor for element .
Step 2.8.1
The minor for is the determinant with row and column deleted.
Step 2.8.2
Evaluate the determinant.
Step 2.8.2.1
The determinant of a matrix can be found using the formula .
Step 2.8.2.2
Simplify the determinant.
Step 2.8.2.2.1
Simplify each term.
Step 2.8.2.2.1.1
Multiply by .
Step 2.8.2.2.1.2
Multiply by .
Step 2.8.2.2.2
Subtract from .
Step 2.9
Calculate the minor for element .
Step 2.9.1
The minor for is the determinant with row and column deleted.
Step 2.9.2
Evaluate the determinant.
Step 2.9.2.1
The determinant of a matrix can be found using the formula .
Step 2.9.2.2
Simplify the determinant.
Step 2.9.2.2.1
Simplify each term.
Step 2.9.2.2.1.1
Multiply by .
Step 2.9.2.2.1.2
Multiply by .
Step 2.9.2.2.2
Subtract from .
Step 2.10
The cofactor matrix is a matrix of the minors with the sign changed for the elements in the positions on the sign chart.