Precalculus 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.
Tap for more steps...
Step 2.1
Calculate the minor for element .
Tap for more steps...
Step 2.1.1
The minor for is the determinant with row and column deleted.
Step 2.1.2
Evaluate the determinant.
Tap for more steps...
Step 2.1.2.1
The determinant of a matrix can be found using the formula .
Step 2.1.2.2
Simplify the determinant.
Tap for more steps...
Step 2.1.2.2.1
Simplify each term.
Tap for more steps...
Step 2.1.2.2.1.1
Multiply by .
Step 2.1.2.2.1.2
Multiply .
Tap for more steps...
Step 2.1.2.2.1.2.1
Multiply by .
Step 2.1.2.2.1.2.2
Multiply by .
Step 2.1.2.2.2
Add and .
Step 2.2
Calculate the minor for element .
Tap for more steps...
Step 2.2.1
The minor for is the determinant with row and column deleted.
Step 2.2.2
Evaluate the determinant.
Tap for more steps...
Step 2.2.2.1
The determinant of a matrix can be found using the formula .
Step 2.2.2.2
Simplify the determinant.
Tap for more steps...
Step 2.2.2.2.1
Simplify each term.
Tap for more steps...
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 .
Tap for more steps...
Step 2.3.1
The minor for is the determinant with row and column deleted.
Step 2.3.2
Evaluate the determinant.
Tap for more steps...
Step 2.3.2.1
The determinant of a matrix can be found using the formula .
Step 2.3.2.2
Simplify the determinant.
Tap for more steps...
Step 2.3.2.2.1
Simplify each term.
Tap for more steps...
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 .
Tap for more steps...
Step 2.4.1
The minor for is the determinant with row and column deleted.
Step 2.4.2
Evaluate the determinant.
Tap for more steps...
Step 2.4.2.1
The determinant of a matrix can be found using the formula .
Step 2.4.2.2
Simplify the determinant.
Tap for more steps...
Step 2.4.2.2.1
Simplify each term.
Tap for more steps...
Step 2.4.2.2.1.1
Multiply by .
Step 2.4.2.2.1.2
Multiply .
Tap for more steps...
Step 2.4.2.2.1.2.1
Multiply by .
Step 2.4.2.2.1.2.2
Multiply by .
Step 2.4.2.2.2
Subtract from .
Step 2.5
Calculate the minor for element .
Tap for more steps...
Step 2.5.1
The minor for is the determinant with row and column deleted.
Step 2.5.2
Evaluate the determinant.
Tap for more steps...
Step 2.5.2.1
The determinant of a matrix can be found using the formula .
Step 2.5.2.2
Simplify the determinant.
Tap for more steps...
Step 2.5.2.2.1
Simplify each term.
Tap for more steps...
Step 2.5.2.2.1.1
Multiply by .
Step 2.5.2.2.1.2
Multiply by .
Step 2.5.2.2.2
Add and .
Step 2.6
Calculate the minor for element .
Tap for more steps...
Step 2.6.1
The minor for is the determinant with row and column deleted.
Step 2.6.2
Evaluate the determinant.
Tap for more steps...
Step 2.6.2.1
The determinant of a matrix can be found using the formula .
Step 2.6.2.2
Simplify the determinant.
Tap for more steps...
Step 2.6.2.2.1
Simplify each term.
Tap for more steps...
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 .
Tap for more steps...
Step 2.7.1
The minor for is the determinant with row and column deleted.
Step 2.7.2
Evaluate the determinant.
Tap for more steps...
Step 2.7.2.1
The determinant of a matrix can be found using the formula .
Step 2.7.2.2
Simplify the determinant.
Tap for more steps...
Step 2.7.2.2.1
Simplify each term.
Tap for more steps...
Step 2.7.2.2.1.1
Multiply by .
Step 2.7.2.2.1.2
Multiply by .
Step 2.7.2.2.2
Add and .
Step 2.8
Calculate the minor for element .
Tap for more steps...
Step 2.8.1
The minor for is the determinant with row and column deleted.
Step 2.8.2
Evaluate the determinant.
Tap for more steps...
Step 2.8.2.1
The determinant of a matrix can be found using the formula .
Step 2.8.2.2
Simplify the determinant.
Tap for more steps...
Step 2.8.2.2.1
Simplify each term.
Tap for more steps...
Step 2.8.2.2.1.1
Multiply by .
Step 2.8.2.2.1.2
Multiply by .
Step 2.8.2.2.2
Add and .
Step 2.9
Calculate the minor for element .
Tap for more steps...
Step 2.9.1
The minor for is the determinant with row and column deleted.
Step 2.9.2
Evaluate the determinant.
Tap for more steps...
Step 2.9.2.1
The determinant of a matrix can be found using the formula .
Step 2.9.2.2
Simplify the determinant.
Tap for more steps...
Step 2.9.2.2.1
Simplify each term.
Tap for more steps...
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.
Enter YOUR Problem
Mathway requires javascript and a modern browser.