# Linear Algebra Examples

Find the Inverse of the Resulting Matrix
Step 1
Step 2
Simplify each element of the matrix .
Simplify .
Simplify .
Simplify .
Simplify .
Step 3
The inverse of a matrix can be found using the formula where is the determinant of .
If then
Step 4
Find the determinant of .
These are both valid notations for the determinant of a matrix.
The determinant of a matrix can be found using the formula .
Simplify the determinant.
Simplify each term.
Multiply by .
Multiply by .
Step 5
Substitute the known values into the formula for the inverse of a matrix.
Step 6
Simplify each element in the matrix.
Rearrange .
Rearrange .
Step 7
Multiply by each element of the matrix.
Step 8
Simplify each element in the matrix.
Rearrange .
Rearrange .
Rearrange .
Rearrange .