# Linear Algebra Examples

Set up the determinant by breaking it into smaller components.

Since the matrix is multiplied by , the determinant is .

The determinant of is .

Set up the determinant by breaking it into smaller components.

The determinant of is .

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

Simplify the determinant.

Multiply by .

Subtract from .

Since the matrix is multiplied by , the determinant is .

The determinant of is .

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

Simplify the determinant.

Simplify each term.

Multiply by .

Multiply by .

Simplify the expression.

Subtract from .

Multiply by .

Add and .

Subtract from .

Multiply by .

The determinant of is .

Set up the determinant by breaking it into smaller components.

The determinant of is .

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

Simplify the determinant.

Simplify each term.

Multiply by .

Multiply by .

Simplify the expression.

Subtract from .

Multiply by .

Since the matrix is multiplied by , the determinant is .

The determinant of is .

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

Simplify the determinant.

Simplify each term.

Multiply by .

Multiply by .

Simplify the expression.

Subtract from .

Multiply by .

Add and .

Subtract from .

Since the matrix is multiplied by , the determinant is .

Add and .

Add and .

Add and .