# Linear Algebra Examples

Step 1

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

Step 2

Step 2.1

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

Step 2.2

Simplify the determinant.

Step 2.2.1

Simplify each term.

Step 2.2.1.1

Multiply by .

Step 2.2.1.2

Multiply by .

Step 2.2.2

Subtract from .

Step 3

Since the determinant is non-zero, the inverse exists.

Step 4

Substitute the known values into the formula for the inverse.

Step 5

Divide by .

Step 6

Multiply by each element of the matrix.

Step 7

Step 7.1

Multiply by .

Step 7.2

Multiply by .

Step 7.3

Multiply by .

Step 7.4

Multiply by .