# Linear Algebra Examples

Step 1

Add the corresponding elements.

Step 2

Step 2.1

Subtract from .

Step 2.2

Subtract from .

Step 2.3

Add and .

Step 2.4

Subtract from .

Step 3

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

Step 4

Step 4.1

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

Step 4.2

Simplify the determinant.

Step 4.2.1

Simplify each term.

Step 4.2.1.1

Multiply by .

Step 4.2.1.2

Multiply by .

Step 4.2.2

Add and .

Step 5

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

Step 6

Substitute the known values into the formula for the inverse.

Step 7

Multiply by each element of the matrix.

Step 8

Step 8.1

Combine and .

Step 8.2

Move the negative in front of the fraction.

Step 8.3

Multiply by .

Step 8.4

Cancel the common factor of .

Step 8.4.1

Factor out of .

Step 8.4.2

Cancel the common factor.

Step 8.4.3

Rewrite the expression.

Step 8.5

Multiply by .