# Linear Algebra Examples

Step 1

Subtract the corresponding elements.

Step 2

Add and .

Subtract from .

Subtract from .

Subtract from .

Step 3

The inverse of a matrix can be found using the formula where is the determinant of .

If then

Step 4

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 .

Add and .

Step 5

Substitute the known values into the formula for the inverse of a matrix.

Step 6

Rearrange .

Rearrange .

Step 7

Multiply by each element of the matrix.

Step 8

Rearrange .

Rearrange .

Rearrange .

Rearrange .