Finite Math Examples

Find the Determinant 5[[8,3,1],[2,4,3],[3,2,4]]
Step 1
Multiply by each element of the matrix.
Step 2
Simplify each element in the matrix.
Tap for more steps...
Step 2.1
Multiply by .
Step 2.2
Multiply by .
Step 2.3
Multiply by .
Step 2.4
Multiply by .
Step 2.5
Multiply by .
Step 2.6
Multiply by .
Step 2.7
Multiply by .
Step 2.8
Multiply by .
Step 2.9
Multiply by .
Step 3
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 3.1
Consider the corresponding sign chart.
Step 3.2
The cofactor is the minor with the sign changed if the indices match a position on the sign chart.
Step 3.3
The minor for is the determinant with row and column deleted.
Step 3.4
Multiply element by its cofactor.
Step 3.5
The minor for is the determinant with row and column deleted.
Step 3.6
Multiply element by its cofactor.
Step 3.7
The minor for is the determinant with row and column deleted.
Step 3.8
Multiply element by its cofactor.
Step 3.9
Add the terms together.
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
Evaluate .
Tap for more steps...
Step 5.1
The determinant of a matrix can be found using the formula .
Step 5.2
Simplify the determinant.
Tap for more steps...
Step 5.2.1
Simplify each term.
Tap for more steps...
Step 5.2.1.1
Multiply by .
Step 5.2.1.2
Multiply by .
Step 5.2.2
Subtract from .
Step 6
Evaluate .
Tap for more steps...
Step 6.1
The determinant of a matrix can be found using the formula .
Step 6.2
Simplify the determinant.
Tap for more steps...
Step 6.2.1
Simplify each term.
Tap for more steps...
Step 6.2.1.1
Multiply by .
Step 6.2.1.2
Multiply by .
Step 6.2.2
Subtract from .
Step 7
Simplify the determinant.
Tap for more steps...
Step 7.1
Simplify each term.
Tap for more steps...
Step 7.1.1
Multiply by .
Step 7.1.2
Multiply by .
Step 7.1.3
Multiply by .
Step 7.2
Add and .
Step 7.3
Subtract from .