Examples

Find the Determinant
Step 1
Choose the row or column with the most elements. If there are no elements choose any row or column. Multiply every element in row by its cofactor and add.
Tap for more steps...
Step 1.1
Consider the corresponding sign chart.
Step 1.2
The cofactor is the minor with the sign changed if the indices match a position on the sign chart.
Step 1.3
The minor for is the determinant with row and column deleted.
Step 1.4
Multiply element by its cofactor.
Step 1.5
The minor for is the determinant with row and column deleted.
Step 1.6
Multiply element by its cofactor.
Step 1.7
The minor for is the determinant with row and column deleted.
Step 1.8
Multiply element by its cofactor.
Step 1.9
Add the terms together.
Step 2
Multiply by .
Step 3
Evaluate .
Tap for more steps...
Step 3.1
The determinant of a matrix can be found using the formula .
Step 3.2
Simplify the determinant.
Tap for more steps...
Step 3.2.1
Simplify each term.
Tap for more steps...
Step 3.2.1.1
Multiply by .
Step 3.2.1.2
Multiply by .
Step 3.2.2
Subtract from .
Step 4
Evaluate .
Tap for more steps...
Step 4.1
The determinant of a matrix can be found using the formula .
Step 4.2
Simplify the determinant.
Tap for more steps...
Step 4.2.1
Simplify each term.
Tap for more steps...
Step 4.2.1.1
Multiply by .
Step 4.2.1.2
Multiply by .
Step 4.2.2
Subtract from .
Step 5
Simplify the determinant.
Tap for more steps...
Step 5.1
Simplify each term.
Tap for more steps...
Step 5.1.1
Multiply by .
Step 5.1.2
Multiply by .
Step 5.2
Add and .
Step 5.3
Subtract from .
Enter YOUR Problem
Mathway requires javascript and a modern browser.