Finite Math Examples

Find the Inverse [[1,0,2],[0,1,-2],[2,0,5]]
Step 1
Find the determinant.
Tap for more steps...
Step 1.1
Choose the row or column with the most elements. If there are no elements choose any row or column. Multiply every element in column by its cofactor and add.
Tap for more steps...
Step 1.1.1
Consider the corresponding sign chart.
Step 1.1.2
The cofactor is the minor with the sign changed if the indices match a position on the sign chart.
Step 1.1.3
The minor for is the determinant with row and column deleted.
Step 1.1.4
Multiply element by its cofactor.
Step 1.1.5
The minor for is the determinant with row and column deleted.
Step 1.1.6
Multiply element by its cofactor.
Step 1.1.7
The minor for is the determinant with row and column deleted.
Step 1.1.8
Multiply element by its cofactor.
Step 1.1.9
Add the terms together.
Step 1.2
Multiply by .
Step 1.3
Multiply by .
Step 1.4
Evaluate .
Tap for more steps...
Step 1.4.1
The determinant of a matrix can be found using the formula .
Step 1.4.2
Simplify the determinant.
Tap for more steps...
Step 1.4.2.1
Simplify each term.
Tap for more steps...
Step 1.4.2.1.1
Multiply by .
Step 1.4.2.1.2
Multiply by .
Step 1.4.2.2
Subtract from .
Step 1.5
Simplify the determinant.
Tap for more steps...
Step 1.5.1
Multiply by .
Step 1.5.2
Add and .
Step 1.5.3
Add and .
Step 2
Since the determinant is non-zero, the inverse exists.
Step 3
Set up a matrix where the left half is the original matrix and the right half is its identity matrix.
Step 4
Find the reduced row echelon form.
Tap for more steps...
Step 4.1
Perform the row operation to make the entry at a .
Tap for more steps...
Step 4.1.1
Perform the row operation to make the entry at a .
Step 4.1.2
Simplify .
Step 4.2
Perform the row operation to make the entry at a .
Tap for more steps...
Step 4.2.1
Perform the row operation to make the entry at a .
Step 4.2.2
Simplify .
Step 4.3
Perform the row operation to make the entry at a .
Tap for more steps...
Step 4.3.1
Perform the row operation to make the entry at a .
Step 4.3.2
Simplify .
Step 5
The right half of the reduced row echelon form is the inverse.